Abstract:
An improved image processing system involves decoding compressed image data including frequency domain coefficients defining blocks of pixel values representing an image at a first resolution to provide an image at a reduced second resolution for display from a selected sub-set of the frequency domain coefficients. The apparatus includes an enhanced motion-compensation-unit (MCU) operating with blocks of pixel values representing an image at an intermediate third resolution lower than the first resolution but higher than the reduced second resolution.

Description:
This is a non-provisional application of provisional application Ser. No. 60/133,429 by M. L. Corner et al, filed 11 May 1999. 

   FIELD OF THE INVENTION 
   The present invention relates to the decoding of a coded high-definition (HD) video signal to derive an enhanced decoded video signal suitable, for example, for recording or producing a picture-in-picture (PIP) or other reduced-resolution display. 
   DESCRIPTION OF THE PRIOR ART 
   Known in the art are television receivers that, while displaying a relatively large picture derived from a primary television channel, also simultaneously display a small picture-in-picture (PIP) derived from a secondary television channel. In the case of a high-definition television (HDTV) receiver, the receiver must include a relatively complex and expensive decoder that conforms with the MPEG ISO 13818-2 standard for decoding a received coded HD video signal in real time for high definition display. However, because the PIP is small, there is no need to provide a high definition PIP display because a viewer inherently would not be able to resolve the higher definition components of a high definition PIP. Therefore, to provide the PIP, the HDTV receiver may be supplied with a lower-resolution second simpler and less expensive decoder which still conforms with the ISO 13818-2 standard. 
   One approach, known in the art, to providing a lower-resolution second decoder which is somewhat simpler and less expensive than the decoder providing the high definition display, is disclosed in the three U.S. Pat. Nos. 5,614,952, 5,614,957 and 5,635,985, which were, respectively, issued to Boyce et al. on Mar. 25, 1997, Mar. 25, 1997 and Jun. 3, 1997. 
   Further, incorporated herein by reference is the teaching of copending U.S. patent application Ser. No. 09/349,865, filed Jul. 8, 1999 and assigned to the same assignee as the present application, which is directed to a lower-resolution second-decoder approach suitable for deriving a PIP display in real time from a received coded HD video signal that is significantly simpler and less expensive to implement than is the second decoder disclosed by Boyce et al, but still conforms with the ISO 13818-2 standard. 
   SUMMARY OF THE INVENTION 
   A system involves decoding compressed image data including frequency domain coefficients defining blocks of pixel values representing an image at a first resolution to provide an image at a reduced second resolution. The system includes a motion-compensation-unit (MCU) processor responsive to a selected sub-set of the frequency domain coefficients for deriving the image of the reduced second resolution. The motion-compensation-unit (MCU) processor employs blocks of pixel values representing image data at an intermediate third resolution lower than the first resolution and higher than the reduced second resolution. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
       FIG. 1  is a functional block diagram showing a variable-length decoder (VLD) responsive to an input HD MPEG data bit-stream for providing a first selected MPEG data output to a PIP decoding means and a second selected MPEG data output to an HD decoding means; 
       FIG. 1   a  shows an 8×8 block containing the 64 DCT coefficients that are employed by the HD decoding means of  FIG. 1 ,  FIG. 1   b  shows an 8×8 block containing the particular 10 DCT coefficients of the 64 DCT coefficients shown in  FIG. 1   a  that are employed by the PIP decoding means of  FIG. 1  for progressive-scan sequences and  FIG. 1   c  shows an 8×8 block containing the particular 10 DCT coefficients of the 64 DCT coefficients shown in  FIG. 1   a  that are employed by the PIP decoding means of  FIG. 1  for interlaced-scan sequences; 
       FIG. 2  is a simplified functional block diagram of an embodiment of the PIP decoding means of  FIG. 1  which incorporates features of the present invention; 
       FIG. 3  is a functional block diagram showing details of the enhanced MCU processing means of  FIG. 2 . 
       FIG. 4  is a conceptual diagram showing the computational processing performed by the DCT-based upsample means of  FIG. 3 ; and 
       FIG. 5  is a conceptual diagram showing the computational processing performed by the DCT-based downsample means of  FIG. 3 . 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Referring to  FIG. 1 , there is shown VLD  100 , PIP decoding means  102  and HD decoding means  104 . In accordance with the known teaching of the MPEG ISO 13818-2 standard, one of the responses of VLD  100  to the input coded HD MPEG data comprising a sequence of MPEG I, P and B frames is to convey coded picture information defined by each of successive 8×8 blocks of quantized discrete cosine transform (DCT) coefficients as an input to HD decoding means  104 . Further, in accordance with the known teaching of the MPEG ISO 13818-2 standard, among the functions performed by HD decoding means  104  is to first perform inverse quantization of each successive 8×8 block of DCT coefficients and then perform inverse discrete cosine transformation (IDCT) of the DCT coefficients of each successive 8×8 block. Finally, HD decoding means  104  must perform motion compensation for each P frame and bi-directionally predictive B frame after IDCT has been performed on that P or B frame. 
     FIG. 1   a  shows an 8×8 block of DCT coefficients, wherein (1) the value of coefficient DCT 0,0  (located in the upper left corner of the 8×8 block) represents the average (DC) value (i.e., both the horizontal and vertical frequencies are 0) of the picture defined by the 64 values of a corresponding 8×8 block of pixels prior to having undergone DCT, while (2) the value of coefficient DCT 7,7  (located in the lower right corner of the 8×8 block) represents the highest horizontal frequency and highest vertical frequency components of the picture defined by the 64 values of a corresponding 8×8 block of pixels prior to having undergone DCT. For the case of a HD picture, all, or nearly all, of the 64 DCT coefficients from DCT 0,0  to DCT 7,7  inclusive of  FIG. 1   a  may have non-zero values. This results in a relatively large amount of image-processing computation to accomplish IDCT in real time. Further, motion compensation also involves a large amount of real time image-processing computation. Therefore, HD decoding means  104  requires about 96 Mbits memory to temporarily store MPEG decoded image frames prior to display. HD decoding means  104  requires these frames for motion compensation to reconstruct accurate images for display. Thus, a physical implementation of HD decoding means  104  is relatively expensive. 
   Returning to  FIG. 1 , another of the responses of VLD  100  to the input coded HD MPEG data is to convey only coded picture information defined by a relatively small given number of lower-frequency-defining, quantized DCT coefficients of each successive 8×8 block as an input to PIP decoding means  102 . It is to be noted that the PIP processing and images and the term PIP itself is used herein to encompass any form of reduced resolution image and processing and not just television PIP image generation. While the preferred tutorial example of the PIP decoding means described in the aforesaid patent application Ser. No. 09/349,865 employed only the 6 lowest-frequency quantized DCT coefficients, the preferred tutorial example of enhanced-quality PIP decoding means  102 , described in detail below, employs 10 DCT coefficients consisting of DCT 0,0 , DCT 1,0 , DCT 2,0 , DCT 3,0 , DCT 0,1 , DCT 1,1 , DCT 2,1 , DCT 0,2 , DCT 1,2 , and DCT 0,3  shown in  FIG. 1   b  for progressive-scan use or, alternatively, consisting of DCT 0,0 , DCT 1,0 , DCT 2,0 , DCT 0,1 , DCT 1,1 , DCT 0,2 , DCT 0,3 , DCT 0,4 , DCT 0,5 , and DCT 0,6  shown in  FIG. 1   c  for interlaced-scan use, thereby providing better high-frequency response for the enhanced PIP display. More specifically, the PIP bit-stream received by VLD  100  has been pre-parsed by a VLD-PIP parser (not shown to simplify  FIG. 1 ) to remove from the bitstream DCT coefficients which are not needed by the PIP decoder. 
   The simplified functional block diagram of the embodiment of enhanced-quality PIP decoding means  102  shown in  FIG. 2  comprises runlength decoder (RLD)  200 , inverse quantizer (IQ)  202 , unitary enhanced IDCT, filtering and pixel-decimation processing means  204 , base-layer adder  205 B, enhancement-layer adder  205 E, base and enhancement-layer decimated pixel memory  206 , enhancement-layer encoder  207 , enhanced motion compensation unit (MCU) processing means  208  and sample-rate converter  210 . Although the simplified functional block diagram of  FIG. 2  does not show means for controlling the operation of this embodiment of enhanced-quality PIP decoding means  102 , it should be understood that suitable control means that conform with the requirements of the ISO 13818-2 standard is included in a physical implementation of this embodiment. 
   For illustrative purposes, the following description of elements  200 ,  202 ,  204 ,  205 B,  205 E,  206 ,  207 ,  208  and  210  assumes that each of these elements is being operated in accordance with the above-discussed preferred tutorial example. 
   In this example, RLD  200  outputs 10 DCT coefficients for each 8×8 coded block using the 2 scan patterns defined in the ISO 13818-2 standard. The positioning of the 10 DCT coefficients within each 8×8 block is illustrated in  FIG. 1   b  for progressive scan and in  FIG. 1   c  for interlaced scan, as determined by the state of the progressive — sequence flag. In the  FIG. 1   b  progressive sequence case, if the alternate — scan flag from the picture coding extension for the current picture is 0, the 10 DCT coefficients correspond to coefficients 0,1,2,3,4,5,6,7,8,9 in 1-dimensional scan order, whereas if alternate — scan is 1, the 10 DCT coefficients of interest are coefficients 0,1,2,3,4,5,6,7,8,20 in scan order. In the  FIG. 1   c  interlaced sequence case, if the alternate — scan flag from the picture coding extension for the current picture is 0, the 10 DCT coefficients correspond to coefficients 0,1,2,3,4,5,9,10,20,21 in 1-dimensional scan order, whereas if alternate — scan is 1, the 10 DCT coefficients of interest are coefficients 0,1,2,3,4,5,6,10,11,12 in scan order. There are two run values that have a meaning in RLD  200  which is different from that described in the ISO 13818-2 standard, depending on the value of the alternate — scan and progressive — sequence flags. For progressive sequences, if alternate — scan is 0, a run value of 10 indicates that the coefficients needed by PIP decoder  102  are all 0 and there is no subsequent non-zero coefficient. Similarly, if alternate — scan is 1, a run value of 21 indicates that the coefficients needed by decoder  102  are all 0 and there is no subsequent non-zero coefficient. For interlaced sequences, if alternate — scan is 0, a run value of 22 indicates that the coefficients needed by PIP decoder  102  are all 0 and there is no subsequent non-zero coefficient. Similarly, if alternate — scan is 1, a run value of 13 indicates that the coefficients needed by decoder  102  are all 0 and there is no subsequent non-zero coefficient. Table 1, summarizes the meaning of run values of 10 and 21 for the two possible values of the alternate — scan flag for progressive sequence and Table 2, summarizes the meaning of run values of 13 and 22 for the two possible values of the alternate — scan flag for interlaced sequence. All other alternate — scan/run value combinations encountered by RLD  200  are interpreted as described in the ISO 13818-2 standard. 
   
     
       
             
           
             
             
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Interpretation of run = 10 and run = 21 by RLD 200 
             
             
               for progressive sequences 
             
           
        
         
             
                 
               Run 
               Alternate — Scan 
               Interpretation in PIP RLD 
             
             
                 
                 
             
             
                 
               10 
               0 
               All DCT coefficients = 0 
             
             
                 
               10 
               1 
               Same as ISO 13818-2 standard 
             
             
                 
               21 
               0 
               Not allowed 
             
             
                 
               21 
               1 
               All DCT coefficients = 0 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
           
         
             
               TABLE 2 
             
           
           
             
                 
             
             
               Interpretation of run = 13 and run = 22 by RLD 200 
             
             
               for interlaced sequences 
             
           
        
         
             
                 
               Run 
               Alternate — Scan 
               Interpretation in PIP RLD 
             
             
                 
                 
             
             
                 
               13 
               0 
               Same as ISO 13818-2 standard 
             
             
                 
               13 
               1 
               All DCT coefficients = 0 
             
             
                 
               22 
               0 
               All DCT coefficients = 0 
             
             
                 
               22 
               1 
               Not allowed 
             
             
                 
                 
             
           
        
       
     
   
   IQ  202  performs inverse quantization arithmetic and saturation described in the ISO 13818-2 standard on the 10 DCT coefficients shown in  FIG. 1   b  for progressive sequences and shown in  FIG. 1   c  for interlaced sequences. The mismatch control portion of the inverse quantization process is not needed. Conventionally, an extensive computational process requiring three separate steps is needed to convert the coded frequency domain information in an 8×8 block at the output from IQ  202 , into spatial domain picture information comprising respective values of a smaller block of decimated pixels of a reduced-resolution PIP display image. The first step is to determine the value of each of the 64 (i.e., full pixel density) pixel values of each 8×8 block of picture information as an IDCT function of the inversely-quantized DCT coefficient values. Thereafter, the second step of lowpass filtering followed by the third step of pixel decimation may be performed on the pixels in each successive 8×8 block to provide the desired smaller block of decimated pixels. For instance, a decimation of alternate horizontal and vertical filtered pixels for the case of a progressive scan would result in a 75% reduction in pixel density. Similarly, a decimation of 3 out of 4 successive filtered pixels in the horizontal direction for the case of an interlaced scan would also result in a 75% reduction in pixel density. Thus, in either case, such a decimation performed for luma pixels and also for chroma pixels would result in a reduction in pixel density from 64 per 8×8 block to only 16 per 8×8 block for each of them. However, the amount of hardware required to implement this conventional three-step computational process is relatively large and, therefore, relatively expensive. 
   In accordance with the principles of the invention taught in the aforesaid patent application Ser. No. 09/349,865, the unitary IDCT, filtering and pixel-decimation processing means disclosed therein is able to convert the coded respective values of inversely-quantized DCT coefficients contained in an 8×8 block at the output from IQ  202 , into a smaller block of decimated pixels in a single-step computational process. Thus, the amount of hardware required to implement this single-step computational process by means  204  is relatively small and, therefore, relatively inexpensive compared to the aforesaid conventional three-step computational process. 
   Specifically, in accordance with the teachings of the aforesaid patent application Ser. No. 09/349,865, the decimated pixel memory thereof (which, because of pixel decimation, requires a storage capacity size of only ¼ the capacity size of a corresponding undecimated pixel memory) comprises a plurality of separate buffers. Each of these buffers is capable of temporarily storing decimated luma and chroma pixels. In conformity with the ISO 13818-2 standard, the decimated pixel memory includes one or more buffers for storing decimated pixels that define reconstructed intracoded (I), predictive-coded (P) and/or bi-directionally predictive-coded (B) frame or field pictures. Further, motion-compensated prediction macroblock output of pixel values from the MCU processing means is added in an adder to each corresponding macroblock output derived in the unitary IDCT, filtering and pixel-decimation processing means. The summed pixel values of the output from the adder are stored into a first buffer of the decimated pixel memory. This first buffer may be a first-in first-out (FIFO) buffer in which the stored decimated pixels may be reordered between (1) being written into the first buffer and (2) being read out from the first buffer and written into another buffer of the decimated pixel memory. In the case of a current P or B frame or field, the decimated pixel memory includes a buffer for storing a macroblock for input to the MCU processing means to provide motion compensation. 
   In accordance with the principles of the present invention, two layers of decimated pixels are advantageously stored respectively in base and enhancement-layer decimated pixel memory  206  to achieve high-quality motion compensation and improve PIP image quality. The first of these two layers is a base-layer of decimated pixels and the second of these two layers is an enhancement-layer of vector-quantized values of luma macroblock decimated pixels that are employed in enhanced MCU processing means  208  during decoding of P pictures The enhanced layer is used to provide a reduced resolution image of greater resolution than is obtainable by using just the decimated pixels of the base-layer. Both the base-layer and this enhancement-layer are employed by enhanced MCU processing means  208 , in a manner described in detail below. 
   Preferred embodiments of IDCT, filtering and pixel-decimation processing means  204 , enhancement-layer encoder  207  and enhanced MCU processing means  208  for implementing the present invention will now be described in detail. 
   The unitary enhanced IDCT, filtering and pixel-decimation processing means  204  provides the following sets of 16 decimated pixel values for each of the base and enhancement-layers used for each of progressive scan and interlaced scan (each set being a function of 10 DCT coefficient values).
 
Progressive-Scan, Base-Layer Set of Decimated Pixel Values 
                 g   1     ⁡     (     0   ,   0     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     10   ⁢     DCT     1   ,   0         +     7   ⁢     DCT     2   ,   0         +     4   ⁢     DCT     3   ,   0         +     10   ⁢     DCT     0   ,   1         +                         ⁢       13   ⁢     DCT     1   ,   1         +     9   ⁢     DCT     2   ,   1         +     7   ⁢     DCT     0   ,   2         +     9   ⁢     DCT     1   ,   2         +     4   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     1   ,   0     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     4   ⁢     DCT     1   ,   0         -     7   ⁢     DCT     2   ,   0         -     9   ⁢     DCT     3   ,   0         +     10   ⁢     DCT     0   ,   1         +                         ⁢       5   ⁢     DCT     1   ,   1         -     9   ⁢     DCT     2   ,   1         +     7   ⁢     DCT     0   ,   2         +     4   ⁢     DCT       1   ,   2     ⁢                 +     4   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     2   ,   0     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     4   ⁢     DCT     1   ,   0         -     7   ⁢     DCT     2   ,   0         +     9   ⁢     DCT     3   ,   0         +     10   ⁢     DCT     0   ,   1         -                         ⁢       5   ⁢     DCT     1   ,   1         -     9   ⁢     DCT     2   ,   1         +     7   ⁢     DCT     0   ,   2         -     4   ⁢     DCT     1   ,   2         +     4   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     3   ,   0     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     10   ⁢     DCT     1   ,   0         +     7   ⁢     DCT     2   ,   0         -     4   ⁢     DCT     3   ,   0         +     10   ⁢     DCT     0   ,   1         -                         ⁢       13   ⁢     DCT     1   ,   1         +     9   ⁢     DCT     2   ,   1         +     7   ⁢     DCT     0   ,   2         -     9   ⁢     DCT     1   ,   2         +     4   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     0   ,   1     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     10   ⁢     DCT     1   ,   0         +     7   ⁢     DCT     2   ,   0         +     4   ⁢     DCT     3   ,   0         +     4   ⁢     DCT     0   ,   1         +                         ⁢       5   ⁢     DCT     1   ,   1         +     4   ⁢     DCT     2   ,   1         -     7   ⁢     DCT     0   ,   2         -     9   ⁢     DCT     1   ,   2         -     9   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     1   ,   1     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     4   ⁢     DCT     1   ,   0         -     7   ⁢     DCT     2   ,   0         -     9   ⁢     DCT     3   ,   0         +     4   ⁢     DCT     0   ,   1         +                         ⁢       2   ⁢     DCT     1   ,   1         -     4   ⁢     DCT     2   ,   1         -     7   ⁢     DCT     0   ,   2         -     4   ⁢     DCT     1   ,   2         -     9   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     2   ,   1     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     4   ⁢     DCT     1   ,   0         -     7   ⁢     DCT     2   ,   0         +     9   ⁢     DCT     3   ,   0         +     4   ⁢     DCT     0   ,   1         -                         ⁢       2   ⁢     DCT     1   ,   1         -     4   ⁢     DCT     2   ,   1         -     7   ⁢     DCT     0   ,   2         +     4   ⁢     DCT     1   ,   2         -     9   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     3   ,   1     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     10   ⁢     DCT     1   ,   0         +     7   ⁢     DCT     2   ,   0         -     4   ⁢     DCT     3   ,   0         +     4   ⁢     DCT     0   ,   1         -                         ⁢       5   ⁢     DCT     1   ,   1         +     4   ⁢     DCT     2   ,   1         -     7   ⁢     DCT     0   ,   2         +     9   ⁢     DCT     1   ,   2         -     9   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     0   ,   2     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     10   ⁢     DCT     1   ,   0         +     7   ⁢     DCT     2   ,   0         +     4   ⁢     DCT     3   ,   0         -     4   ⁢     DCT     0   ,   1         -                         ⁢       5   ⁢     DCT     1   ,   1         -     4   ⁢     DCT     2   ,   1         -     7   ⁢     DCT     0   ,   2         -     9   ⁢     DCT     1   ,   2         +     9   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     1   ,   2     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     4   ⁢     DCT     1   ,   0         -     7   ⁢     DCT     2   ,   0         -     9   ⁢     DCT     3   ,   0         -     4   ⁢     DCT     0   ,   1         -                         ⁢       2   ⁢     DCT     1   ,   1         +     4   ⁢     DCT     2   ,   1         -     7   ⁢     DCT     0   ,   2         -     4   ⁢     DCT     1   ,   2         +     9   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     2   ,   2     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     4   ⁢     DCT     1   ,   0         -     7   ⁢     DCT     2   ,   0         +     9   ⁢     DCT     3   ,   0         -     4   ⁢     DCT     0   ,   1         +                         ⁢       2   ⁢     DCT     1   ,   1         +     4   ⁢     DCT     2   ,   1         -     7   ⁢     DCT     0   ,   2         +     4   ⁢     DCT     1   ,   2         +     9   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     3   ,   2     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     10   ⁢     DCT     1   ,   0         +     7   ⁢     DCT     2   ,   0         -     4   ⁢     DCT     3   ,   0         -     4   ⁢     DCT     0   ,   1         +                         ⁢       5   ⁢     DCT     1   ,   1         -     4   ⁢     DCT     2   ,   1         -     7   ⁢     DCT     0   ,   2         +     9   ⁢     DCT     1   ,   2         +     9   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     0   ,   3     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     10   ⁢     DCT     1   ,   0         +     7   ⁢     DCT     2   ,   0         +     4   ⁢     DCT     3   ,   0         -     10   ⁢     DCT     0   ,   1         -                         ⁢       13   ⁢     DCT     1   ,   1         -     9   ⁢     DCT     2   ,   1         +     7   ⁢     DCT     0   ,   2         +     9   ⁢     DCT     1   ,   2         -     4   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     1   ,   3     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     4   ⁢     DCT     1   ,   0         -     7   ⁢     DCT     2   ,   0         -     9   ⁢     DCT     3   ,   0         -     10   ⁢     DCT     0   ,   1         -                         ⁢       5   ⁢     DCT     1   ,   1         +     9   ⁢     DCT     2   ,   1         +     7   ⁢     DCT     0   ,   2         +     4   ⁢     DCT     1   ,   2         -     4   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     2   ,   3     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     4   ⁢     DCT     1   ,   0         -     7   ⁢     DCT     2   ,   0         +     9   ⁢     DCT     3   ,   0         -     10   ⁢     DCT     0   ,   1         +                         ⁢       5   ⁢     DCT     1   ,   1         +     9   ⁢     DCT     2   ,   1         +     7   ⁢     DCT     0   ,   2         -     4   ⁢     DCT     1   ,   2         -     4   ⁢     DCT     0   ,   3           ]     /   64                   g   1     ⁡     (     3   ,   3     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     10   ⁢     DCT     1   ,   0         +     7   ⁢     DCT     2   ,   0         -     4   ⁢     DCT     3   ,   0         -     10   ⁢     DCT     0   ,   1         +                         ⁢       13   ⁢     DCT     1   ,   1         -     9   ⁢     DCT     2   ,   1         +     7   ⁢     DCT     0   ,   2         -     9   ⁢     DCT     1   ,   2         -     4   ⁢     DCT     0   ,   3           ]     /   64             
 
Progressive-Scan, Enhancement-Layer Set of Decimated PIXEL Values 
                 g   0     ⁡     (     0   ,   0     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     1   ⁢     DCT     0   ,   1         +                         ⁢       1   ⁢     DCT     1   ,   1         +     1   ⁢     DCT     2   ,   1         +     3   ⁢     DCT     0   ,   2         +     4   ⁢     DCT     1   ,   2         +     6   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     1   ,   0     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     1   ⁢     DCT     0   ,   1         +                         ⁢       0   ⁢     DCT     1   ,   1         -     1   ⁢     DCT     2   ,   1         +     3   ⁢     DCT     0   ,   2         +     2   ⁢     DCT     1   ,   2         +     6   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     2   ,   0     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     1   ⁢     DCT     0   ,   1         +                         ⁢       0   ⁢     DCT     1   ,   1         -     1   ⁢     DCT     2   ,   1         +     3   ⁢     DCT     0   ,   2         -     2   ⁢     DCT     1   ,   2         +     6   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     3   ,   0     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     1   ⁢     DCT     0   ,     1   -                                 ⁢       1   ⁢     DCT     1   ,   1         +     1   ⁢     DCT     2   ,   1         +     3   ⁢     DCT     0   ,   2         -     4   ⁢     DCT     1   ,   2         +     6   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     0   ,   2     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     2   ⁢     DCT     0   ,   1         +                         ⁢       3   ⁢     DCT     1   ,   1         +     2   ⁢     DCT     2   ,   1         +     3   ⁢     DCT     0   ,   2         +     4   ⁢     DCT     1   ,   2         -     2   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     1   ,   2     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     2   ⁢     DCT     0   ,   1         +                         ⁢       1   ⁢     DCT     1   ,   1         -     2   ⁢     DCT     2   ,   1         +     3   ⁢     DCT     0   ,   2         +     2   ⁢     DCT     1   ,   2         -     2   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     2   ,   2     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     2   ⁢     DCT     0   ,   1         -                         ⁢       1   ⁢     DCT     1   ,   1         -     2   ⁢     DCT     2   ,   1         +     3   ⁢     DCT     0   ,   2         -     2   ⁢     DCT     1   ,   2         -     2   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     3   ,   2     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     2   ⁢     DCT     0   ,   1         -                         ⁢       3   ⁢     DCT     1   ,   1         +     2   ⁢     DCT     2   ,   1         +     3   ⁢     DCT     0   ,   2         -     4   ⁢     DCT     1   ,   2         -     2   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     0   ,   4     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     2   ⁢     DCT     0   ,   1         +                         ⁢       3   ⁢     DCT     1   ,   1         +     2   ⁢     DCT     2   ,   1         -     3   ⁢     DCT     0   ,   2         -     4   ⁢     DCT     1   ,   2         -     2   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     1   ,   4     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     2   ⁢     DCT     0   ,   1         +                         ⁢       1   ⁢     DCT     1   ,   1         -     2   ⁢     DCT     2   ,   1         -     3   ⁢     DCT     0   ,   2         -     2   ⁢     DCT     1   ,   2         -     2   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     2   ,   4     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     2   ⁢     DCT     0   ,   1         -                         ⁢       1   ⁢     DCT     1   ,   1         -     2   ⁢     DCT     2   ,   1         -     3   ⁢     DCT     0   ,   2         +     2   ⁢     DCT     1   ,   2         -     2   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     3   ,   4     )       =       ⁢       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     2   ⁢     DCT     0   ,   1         -                       ⁢       3   ⁢     DCT     1   ,   1         +     2   ⁢     DCT     2   ,   1         -     3   ⁢     DCT     0   ,   2         +     4   ⁢     DCT     1   ,   2         -     2   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     0   ,   6     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     1   ⁢     DCT     0   ,   1         +                         ⁢       1   ⁢     DCT     1   ,   1         +     1   ⁢     DCT     2   ,   1         -     3   ⁢     DCT     0   ,   2         +     49   ⁢     DCT     1   ,   2         +     6   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     1   ,   6     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     1   ⁢     DCT     0   ,   1         +                         ⁢       0   ⁢     DCT     1   ,   1         -     1   ⁢     DCT     2   ,   1         -     3   ⁢     DCT     0   ,   2         -     2   ⁢     DCT     1   ,   2         +     6   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     2   ,   6     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     1   ⁢     DCT     0   ,   1         +                         ⁢       0   ⁢     DCT     1   ,   1         -     1   ⁢     DCT     2   ,   1         -     3   ⁢     DCT     0   ,   2         +     2   ⁢     DCT     1   ,   2         +     6   ⁢     DCT     0   ,   3           ]     /   64                   g   0     ⁡     (     3   ,   6     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     0   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     3   ,   0         +     1   ⁢     DCT     0   ,   1         -                         ⁢       1   ⁢     DCT     1   ,   1         +     1   ⁢     DCT     2   ,   1         -     3   ⁢     DCT     0   ,   2         +     4   ⁢     DCT     1   ,   2         +     6   ⁢     DCT     0   ,   3           ]     /   64             
 
Interlaced-Scan, Base-Layer Set of Decimated Pixel Values 
                 g   1     ⁡     (     0   ,   0     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     7   ⁢     DCT     1   ,   0         +     11   ⁢     DCT     0   ,   1         +     10   ⁢     DCT     1   ,   1         +     10   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢     DCT     2   ,   0         +     9   ⁢     DCT     0   ,   3         +     8   ⁢     DCT     0   ,   4         +     6   ⁢     DCT     0   ,   5         +     4   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     1   ,   0     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     7   ⁢     DCT     1   ,   0         +     11   ⁢     DCT     0   ,   1         -     10   ⁢     DCT     1   ,   1         +     10   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         +     9   ⁢     DCT     0   ,   3         +     8   ⁢     DCT     0   ,   4         +     6   ⁢     DCT     0   ,   5         +     4   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     0   ,   1     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     7   ⁢     DCT     1   ,   0         +     9   ⁢     DCT     0   ,   1         +     9   ⁢     DCT     1   ,   1         +     4   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         -     2   ⁢     DCT     0   ,   3         -     8   ⁢     DCT     0   ,   4         -     11   ⁢     DCT     0   ,   5         -     10   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     1   ,   1     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     7   ⁢     DCT     1   ,   0         +     9   ⁢     DCT     0   ,   1         -     9   ⁢     DCT     1   ,   1         +     4   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         -     2   ⁢     DCT     0   ,   3         -     8   ⁢     DCT     0   ,   4         -     11   ⁢     DCT     0   ,   5         -     10   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     0   ,   2     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     7   ⁢     DCT     1   ,   0         +     6   ⁢     DCT     0   ,   1         +     6   ⁢     DCT     1   ,   1         -     4   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         -     11   ⁢     DCT     0   ,   3         -     8   ⁢     DCT     0   ,   4         +     2   ⁢     DCT     0   ,   5         +     10   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     1   ,   2     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     7   ⁢     DCT     1   ,   0         +     6   ⁢     DCT     0   ,   1         -     6   ⁢     DCT     1   ,   1         -     4   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         -     11   ⁢     DCT     0   ,   3         -     8   ⁢     DCT     0   ,   4         +     2   ⁢     DCT     0   ,   5         +     10   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     0   ,   3     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     7   ⁢     DCT     1   ,   0         +     2   ⁢     DCT     0   ,   1         +     2   ⁢     DCT     1   ,   1         -     10   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         -     6   ⁢     DCT     0   ,   3         -     8   ⁢     DCT     0   ,   4         +     9   ⁢     DCT     0   ,   5         -     4   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     1   ,   3     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     7   ⁢     DCT     1   ,   0         +     2   ⁢     DCT     0   ,   1         +     2   ⁢     DCT     1   ,   1         -     10   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         -     6   ⁢     DCT     0   ,   3         +     8   ⁢     DCT     0   ,   4         +     9   ⁢     DCT     0   ,   5         -     4   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     0   ,   4     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     7   ⁢     DCT     1   ,   0         -     2   ⁢     DCT     0   ,   1         -     2   ⁢     DCT     1   ,   1         -     10   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         +     6   ⁢     DCT     0   ,   3         +     8   ⁢     DCT     0   ,   4         -     9   ⁢     DCT     0   ,   5         -     4   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     1   ,   4     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     7   ⁢     DCT     1   ,   0         -     2   ⁢     DCT     0   ,   1         +     2   ⁢     DCT     1   ,   1         -     10   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         +     6   ⁢     DCT     0   ,   3         +     8   ⁢     DCT     0   ,   4         -     9   ⁢     DCT     0   ,   5         -     4   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     0   ,   5     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     7   ⁢     DCT     1   ,   0         -     6   ⁢     DCT     0   ,   1         -     6   ⁢     DCT     1   ,   1         -     4   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         +     11   ⁢     DCT     0   ,   3         -     8   ⁢     DCT     0   ,   4         -     2   ⁢     DCT     0   ,   5         +     10   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     1   ,   5     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     7   ⁢     DCT     1   ,   0         -     6   ⁢     DCT     0   ,   1         +     6   ⁢     DCT     1   ,   1         -     4   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         +     11   ⁢     DCT     0   ,   3         -     8   ⁢     DCT     0   ,   4         -     2   ⁢     DCT     0   ,   5         +     10   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     0   ,   6     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     7   ⁢     DCT     1   ,   0         -     9   ⁢     DCT     0   ,   1         -     9   ⁢     DCT     1   ,   1         +     4   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         +     2   ⁢     DCT     0   ,   3         -     8   ⁢     DCT     0   ,   4         +     11   ⁢     DCT     0   ,   5         -     10   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     1   ,   6     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     7   ⁢     DCT     1   ,   0         -     9   ⁢     DCT     0   ,   1         +     9   ⁢     DCT     1   ,   1         +     4   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         +     2   ⁢     DCT     0   ,   3         -     8   ⁢     DCT     0   ,   4         +     11   ⁢     DCT     0   ,   5         -     10   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     0   ,   7     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         +     7   ⁢     DCT     1   ,   0         -     11   ⁢     DCT     0   ,   1         -     10   ⁢     DCT     1   ,   1         +     10   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         -     9   ⁢     DCT     0   ,   3         +     8   ⁢     DCT     0   ,   4         -     6   ⁢     DCT     0   ,   5         +     4   ⁢     DCT     0   ,   6           ]     /   64                   g   1     ⁡     (     1   ,   7     )       =       ⁢     [       8   ⁢     DCT     0   ,   0         -     7   ⁢     DCT     1   ,   0         -     11   ⁢     DCT     0   ,   1         +     10   ⁢     DCT     1   ,   1         +     10   ⁢     DCT     0   ,   2         +                         ⁢       0   ⁢           ⁢     DCT     2   ,   0         -     9   ⁢     DCT     0   ,   3         +     8   ⁢     DCT     0   ,   4         -     6   ⁢     DCT     0   ,   5         +     4   ⁢     DCT     0   ,   6           ]     /   64             
 
Interlaced-Scan, Enhancement-Layer Set of Decimated Pixel Values 
                 g   0     ⁡     (     0   ,   0     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         +     4   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         +                         ⁢       7   ⁢           ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     2   ,   0     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         +     4   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         -                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     0   ,   1     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         +     4   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         +                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     2   ,   1     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         +     4   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         -                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     0   ,   2     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         +     2   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         +                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     2   ,   2     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         +     2   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         -                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     0   ,   3     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         +     1   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         +                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     2   ,   3     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         +     1   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         -                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     0   ,   4     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         -     1   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         +                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     2   ,   4     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         -     1   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         -                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     0   ,   5     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         -     2   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         +                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     2   ,   5     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         -     2   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         -                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     0   ,   6     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         -     4   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         +                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     2   ,   6     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         -     4   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         -                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     0   ,   7     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         -     4   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         +                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64                   g   0     ⁡     (     2   ,   7     )       =       ⁢     [       0   ⁢     DCT     0   ,   0         +     3   ⁢     DCT     1   ,   0         +     0   ⁢     DCT     0   ,   1         -     4   ⁢     DCT     1   ,   1         +     0   ⁢     DCT     0   ,   2         -                         ⁢       7   ⁢     DCT     2   ,   0         +     0   ⁢     DCT     0   ,   3         +     0   ⁢     DCT     0   ,   4         +     0   ⁢     DCT     0   ,   5         +     0   ⁢     DCT     0   ,   6           ]     /   64             
 
   Each of the above “Progressive-Scan Set of Decimated Pixel Values” and above “Interlaced-Scan Set of Decimated Pixel Values” was derived in the following manner:
         1. If DCT u,ν  denotes the DCT coefficient with horizontal frequency index u and vertical frequency index ν, then the IDCT equation which would be used to decode a block denoted f(x,y) at full resolution (where x=0, . . . ,N−1; y=0, . . . ,N−1) is given by 
               f   ⁡     (     x   ,   y     )       =       2   N     ⁢       ∑     u   =   0       N   -   1       ⁢       ∑     v   =   0       N   -   1       ⁢       C   ⁡     (   u   )       ⁢     C   ⁡     (   v   )       ⁢     DCT     u   ,   v       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢           ⁢   u   ⁢           ⁢   π       2   ⁢   N       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   v   ⁢           ⁢   π       2   ⁢   N                       (   1   )             
   2. Using only the 10 DCT coefficients shown in  FIG. 1   b , gives the approximation equation 2 for progressive-scan sequences 
               f   ⁡     (     x   ,   y     )       ≈       2   N     ⁡     [               1   2     ⁢     DCT     0   ,   0         +       1     2       ⁢     DCT     1   ,   0       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢   π       2   ⁢   N         +                   1     2       ⁢     DCT     2   ,   0       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢   2   ⁢           ⁢   π       2   ⁢   N         +                   1     2       ⁢     DCT     3   ,   0       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢   3   ⁢           ⁢   π       2   ⁢   N         +                   1     2       ⁢     DCT     0   ,   1       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   π       2   ⁢   N         +                   DCT     1   ,   1       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢   π       2   ⁢   N       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   π       2   ⁢   N         +                   1     2       ⁢     DCT     0   ,   2       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   2   ⁢           ⁢   π       2   ⁢   N         +                   DCT     2   ,   1       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢   2   ⁢           ⁢   π       2   ⁢   N       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   π       2   ⁢   N         +                   DCT     1   ,   2       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢   π       2   ⁢   N       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   2   ⁢           ⁢   π       2   ⁢   N         +                 1     2       ⁢     DCT     0   ,   3       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   3   ⁢           ⁢   π       2   ⁢   N               ]               (   2   )             
   3. Using only the 10 DCT coefficients shown in  FIG. 1   c , gives the approximation equation 3 for interlaced-scan sequences 
               f   ⁡     (     x   ,   y     )       ≈       2   N     ⁡     [               1   2     ⁢     DCT     0   ,   0         +       1     2       ⁢     DCT     1   ,   0       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢   π       2   ⁢   N         +                   1     2       ⁢     DCT     2   ,   0       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢   2   ⁢           ⁢   π       2   ⁢   N         +       1     2       ⁢     DCT     0   ,   1       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢           ⁢   π       2   ⁢   N         +                   DCT     1   ,   1       ⁢   cos   ⁢         (       2   ⁢   x     +   1     )     ⁢   π       2   ⁢   N       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   π       2   ⁢   N         +                   1     2       ⁢     DCT     0   ,   2       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   2   ⁢           ⁢   π       2   ⁢   N         +       1     2       ⁢     DCT     0   ,   3       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   3   ⁢           ⁢   π       2   ⁢   N         +                   1     2       ⁢     DCT     0   ,   4       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   4   ⁢           ⁢   π       2   ⁢   N         +       1     2       ⁢       DCT   ⁢               0   ,   5       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   5   ⁢           ⁢   π       2   ⁢   N         +                 1     2       ⁢     DCT     0   ,   6       ⁢   cos   ⁢         (       2   ⁢   y     +   1     )     ⁢   6   ⁢           ⁢   π       2   ⁢   N               ]               (   3   )             
   4. Let the right-hand side of each of equations 2 and 3 be denoted f′(x,y). In the case of a progressive scan (i.e., the progressive — sequence flag is 1), the base-layer value g 1 ′(x,y) is computed in accordance with the following equation 4 and the enhancement-layer value g 0 ′(x,y) is computed in accordance with the following equation 5: 
                   g   1   ′     ⁡     (     x   ,   y     )       =       1   4     ⁡     [         f   ′     ⁡     (       2   ⁢   x     ,     2   ⁢   y       )       +       f   ′     ⁡     (         2   ⁢   x     +   1     ,     2   ⁢   y       )       +       f   ′     ⁡     (       2   ⁢   x     ,       2   ⁢   y     +   1       )       +       f   ′     ⁡     (         2   ⁢   x     +   1     ,       2   ⁢   y     +   1       )         ]         ⁢     
     ⁢         for   ⁢           ⁢   x     =   0     ,   …   ⁢           ,     3   ;     y   =   0       ,   …   ⁢           ,   3.             (   4   )                     g   0   ′     ⁡     (     x   ,   y     )       =       1   4     ⁡     [         f   ′     ⁡     (       2   ⁢   x     ,   y     )       +       f   ′     ⁡     (         2   ⁢   x     +   1     ,   y     )       -       f   ′     ⁡     (       2   ⁢   x     ,     y   +   1       )       -       f   ′     ⁡     (         2   ⁢   x     +   1     ,     y   +   1       )         ]         ⁢     
     ⁢         for   ⁢           ⁢   x     =   0     ,   …   ⁢           ,     3   ;     y   =   0       ,   2   ,   4   ,   6.             (   5   )             
    More specifically, g 1 ′(x,y) in equation 4 defines the average value of the values of a set of 4 contiguous pixels (or prediction errors) arranged in a 2×2 block portion of the full-resolution 8×8 block. The value g 0 ′(x,y) in equation 5 defines the difference between the average value of the values of a first set of 2 contiguous horizontal pixels (or prediction errors) of one vertical line and the average value of the values of a second set of 2 contiguous horizontal pixels (or prediction errors) of the following vertical line arranged in a 2×2 block portion of the full-resolution 8×8 block. The 16 equations g 1 (0,0) to g 1 (3,3) of the above “Progressive-Scan, Base-layer Set of Decimated Pixel Values” were derived by substituting equation 2 into equation 4, substituting numeric values for x and y in g 1 ′(x,y), substituting N=8, and approximating the weighting factors for the DCT coefficients with rational values. The 16 equations g 0 (0,0) to g 0 (3,6) of the above “Progressive-Scan, Enhancement-layer Set of Decimated Pixel Values” were derived in a similar manner by substituting equation 2 into equation 5, substituting numeric values for x and y in g 0 ′(x,y), substituting N=8, and approximating the weighting factors for the DCT coefficients with rational values. Although the effective pixel decimation of the enhancement-layer is only 2 (rather than being the effective pixel decimation of 4 of the base-layer), the equalities g 0 (x,y+1)=−g 0 (x,y) hold for y=0,2,4,6, so that enhancement-layer values with odd vertical indexes need not be computed. Thus, only 16 independent g 0 (x,y) enhancement-layer values need be computed for each 8×8 luma block in a progressive-scan I or P picture. Further, because these 16 g 0 (x,y) enhancement-layer values are residual values, they tend to have a small dynamic range.       

   In the case of an interlaced scan (i.e., the progressive — sequence flag is 0), the base-layer value g 1 ′(x,y) is computed in accordance with the following equation 6 and the enhancement-layer value g 0 ′(x,y) is computed in accordance with the following equation 7: 
                     g   1   ′     ⁡     (     x   ,   y     )       =       1   4     ⁡     [         f   ′     ⁡     (       4   ⁢   x     ,   y     )       +       f   ′     ⁡     (         4   ⁢   x     +   1     ,   y     )       +       f   ′     ⁡     (         4   ⁢   x     +   2     ,   y     )       +       f   ′     ⁡     (         4   ⁢   x     +   3     ,   y     )         ]         ⁢           ⁢         for   ⁢           ⁢   x     =   0     ,     1   ;     y   =   0       ,   …   ⁢           ,   7.       ⁢     
             (   6   )                     g   0   ′     ⁡     (     x   ,   y     )       =       1   4     ⁡     [         f   ′     ⁡     (       2   ⁢   x     ,   y     )       +       f   ′     ⁡     (         2   ⁢   x     +   1     ,   y     )       -       f   ′     ⁡     (         2   ⁢   x     +   2     ,   y     )       -       f   ′     ⁡     (         2   ⁢   x     +   3     ,   y     )         ]         ⁢     
     ⁢         for   ⁢           ⁢   x     =   0     ,     2   ;     y   =   0       ,   …   ⁢           ,   7.             (   7   )             
 
In the interlaced-scan case of an 8×8 block, g 1 ′(x,y) in equation 6 defines the average value of the values of a set of 4 contiguous pixels (or prediction errors) arranged in a 4×1 block portion of the 8×8 block. The value g 0 ′(x,y) in equation 7 defines the difference between the average value of the values of a first set of 2 contiguous horizontal pixels (or prediction errors) of a vertical line and the average value of the values of a second set of the next 2 contiguous horizontal pixels (or prediction errors) of the same vertical line arranged in a 4×1 block portion of an 8×8 block. The 16 equations g 1 (0,0) to g 1 (1,7) of the above “Interlaced-Scan, Base-layer Set of Decimated Pixel Values” were derived by substituting equation 3 into equation 6, substituting numeric values for x and y in g 1 ′(x,y), substituting N=8, and approximating the weighting factors for the DCT coefficients with rational values. The 16 equations g 0 (0,0) to g 0 (2,7) of the above “Interlaced-Scan, Enhancement-layer Set of Decimated Pixel Values” were derived in a similar manner by substituting equation 3 into equation 7, substituting numeric values for x and y in g 0 ′(x,y), substituting N=8, and approximating the weighting factors for the DCT coefficients with rational values. Although the effective pixel decimation of the enhancement-layer is only 2 (rather than the effective pixel decimation of 4 of the base-layer), the equalities g 0 (x+1,y)=−g 0 (x,y) hold for x=0 and x=2 so that enhancement-layer values with odd horizontal indexes need not be computed. Thus, only 16 independent g 0 (x,y) enhancement-layer values need be computed for each 8×8 luma block in an interlaced-scan I or P picture. Further, because these 16 g 0 (x,y) enhancement-layer values are residual values, they tend to have a small dynamic range.
 
   Returning to  FIG. 2 , unit  204  conveys an output comprising successive 8×8 blocks of I, P and B luma and chroma g 1 (x,y) base-layer decimated pixel values as a first input to base-layer adder  205 B in a predetermined order. (For non-coded blocks all such values are zero). This predetermined order includes the decimated pixel values of each 2×2 array of 8×8 pixel luma blocks and each of two chroma blocks which form a decimated macroblock for use by enhanced MCU processing means  208 . Further, unit  208  applies a corresponding block p 1 (x,y) of base-layer decimated pixel values as a second input to base-layer adder  205 B in this same predetermined order (For intra-coded macroblocks all such values are zero). The block s 1 (x,y) of base-layer decimated pixel values derived as a sum output from base-layer adder  205 B are then stored in memory  206 . 
   Unit  204  conveys an output comprising the I and P luma g 0 (x,y) enhancement-layer decimated pixel values as a first input to enhancement-layer adder  205 E in the previously mentioned decimated-pixel macroblock predetermined order. (For non-coded blocks all such values are zero). Further, for the case of P luma pixels, unit  208  applies a corresponding macroblock of 64 p 0 (x,y) enhancement-layer decimated pixel values as a second input to adder  205 E in this same predetermined order. (For intra-coded macroblocks all such values are zero). The macroblock of 64 s 0 (x,y) enhancement-layer decimated pixel values derived as a sum output from adder  205 E are applied as an input to enhancement-layer encoder  207  and then the encoded output bit-words from encoder  207  are stored in memory  206  during decoding of I and P pictures. 
   A macroblock at the higher resolution of the enhancement-layer would normally comprise 128 decimated luma pixel values. However, because of the above-described symmetry equalities for both progressive-scan sequences and interlaced-scan sequences, the number of independent decimated enhancement-layer pixel values in the block s 0 (x,y) is reduced from 128 to 64. Therefore, the predetermined order is such that only half of the enhancement-layer decimated pixel values need be considered by enhancement-layer encoder  207 . These enhancement-layer values are encoded in pairs using a simple vector quantizer, with each pair of values being represented by an 8-bit codeword. Since there are 64 enhancement-layer values to be encoded in a macroblock, the number of bits of storage for the enhancement layer is 32×8=256 bits per macroblock. In the preferred embodiment the 32 codewords are combined into two 128-bit output words from encoder  207  for storage in memory  206 . 
   For progressive sequences each pair of horizontally adjacent values in the block s 0 (x,y) is encoded as a two-dimensional vector, whereas for interlaced sequences each pair of vertically adjacent (within the same field) values in s 0 (x,y) is encoded as a two-dimensional vector. Let v 0  and v 1  be a pair of values to be encoded together. The computational procedure employed by encoder  207  to encode the pair v 0 ,v 1  is described in detail in Appendix A. After this procedure has been completed for each pair of values in s 0 (x,y), the codewords are packed into two 128-bit words, both of which 128-bit words form the output from encoder  207  that are stored in memory  206 . Returning again to  FIG. 2 , memory  206  provides (1) a base-layer output d 1 (x,y) to unit  208  (d 1 (x,y) is similar in content to the base-layer input s 1 (x,y) provided to memory  206 ) and (2) an enhancement-layer output to unit  208  (similar in content to the enhancement-layer input to memory  206 ). 
   In order for enhanced MCU processing means  208  to form a block of predictions, a block of pixel values is fetched from memory  206 . The base-layer of pixel values which are read from the stored reference picture are denoted d 1 (x,y). The enhancement-layer residual values, which are needed only if the block of predictions being formed is for the luma component in a P picture, are denoted d 0 (x,y). Since the enhancement-layer samples are stored in memory  206  in encoded form, the enhancement-layer data output from memory  206  input to unit  208  is decoded by enhancement-layer decoder  300  ( FIG. 3 ) to obtain the d 0 (x,y) values. Unit  208  separately forms individual luma or chroma outputs for field prediction operations corresponding to the top and bottom field prediction blocks. In a bi-directionally predicted macroblock these operations are performed separately for the forward and backward predictions and the results are combined as described in the ISO 13818-2 standard. In the following detailed description of the computational-processing operations performed by unit  208 , the symbol / represents integer division with truncation of the result toward minus infinity, the symbol // represents integer division with truncation of the result toward zero, and the symbol % represents the modulus operator, which is defined such that if x is a negative number and M is a positive number, then x % M=M−((x//M)*M−x). 
   Before a block of samples can be read from memory  206 , the location and size of the block is determined. The location of a block of pixel values in the reference picture is specified by the horizontal and vertical coordinates of the start (i.e., the upper-left corner) of the block in the reference picture. For the base-layer, these coordinates are indexes into a picture which is ¼ horizontal, full vertical resolution for interlaced sequences and ½ horizontal, ½ vertical resolution for progressive sequences. For the enhancement-layer, the coordinates are indexes into a picture which is ½ horizontal, full vertical resolution for both interlaced and progressive sequences. 
   To locate the blocks d 1 (x,y) and d 0 (x,y) in the reference picture, the motion vector for the macroblock being decoded is needed. The decoding of motion vector data in the bitstream, the updating of motion vector predictors, and the selection of motion vectors in non-intra macroblocks which contain no coded motion vectors (e.g., skipped macroblocks) are all performed by unit  208  as described in the ISO 13818-2 standard. Let x b  and y b  be the full-resolution horizontal and vertical positions of the macroblock being decoded and let mv=(dx,dy) be the decoded motion vector, so that if the sequence were being decoded at full resolution, a block of pixel values at location (x b +(dx/2), y b +(dy/2)) in the full-resolution reference luma picture would be read from memory and used to form luma predictions. Similarly, a block of chroma values at location (x b /2+(dx//2), y b /2+(dy//2)) in the reference chroma picture would be needed to form predictions for each of the 2 chroma components in a full-resolution mode. 
   The location in the reference picture of a block needed for motion compensation in unit  208  is determined using x b , y b , dx and dy. Table 3, shows the locations of blocks for various prediction modes. The sizes of the blocks needed for motion compensation in unit  208  are specified in Table 4. Base-layer entries in Table 4 give the size of the block d 1 (x,y), and enhancement-layer entries in Table 4 give the size of the block d 0 (x,y). 
   
     
       
             
           
             
             
             
           
         
             
               TABLE 3 
             
           
           
             
                 
             
             
               Locations of Blocks Needed for Motion Compensation 
             
             
               in Enhanced MCU Processing Means 208 
             
           
        
         
             
                 
               Horizontal 
               Vertical 
             
             
               Prediction Mode 
               Coordinate 
               Coordinate 
             
             
                 
             
             
               Progressive sequence, luma, 
               ((x b  + (dx/2))/8)*4 
               (y b  + (dy/2))/2 
             
             
               base-layer 
             
             
               Progressive sequence, luma, 
               ((x b  + (dx/2))/8)*4 
               ((y b  + (dy/2))/2)*2 
             
             
               enhancement-layer 
             
             
               Progressive sequence, chroma 
               x b /4 + ((dx//2)/4) 
               y b /4 + ((dy//2)/4) 
             
             
               Interlaced sequence, luma, 
               ((x b  + (dx/2))/8)*2 
               y b  + (dy/2) 
             
             
               base-layer 
             
             
               Interlaced sequence, luma, 
               ((x b  + (dx/2))/8)*4 
               y b  + (dy/2) 
             
             
               enhancement-layer 
             
             
               Interlaced sequence, chroma 
               x b /8 + ((dx//2)/8) 
               y b /2 + ((dy//2)/2) 
             
             
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
           
             
             
             
           
         
             
               TABLE 4 
             
           
           
             
                 
             
             
               Sizes of Blocks Needed for Motion Compensation 
             
             
               in Enhanced MCU Processing Means 208 
             
           
        
         
             
                 
               Horizontal 
               Vertical 
             
             
               Prediction Mode 
               Size 
               Size 
             
             
                 
             
           
        
         
             
               Progressive sequence, luma, base-layer 
               12 
               9 
             
             
               Progressive sequence, luma, enhancement-layer 
               12 
               18 
             
             
               Progressive sequence, chroma 
               5 
               5 
             
             
               Interlaced sequence, luma, 16 × 16 prediction, 
               6 
               17 
             
             
               base-layer 
             
             
               Interlaced sequence, luma, 16 × 8 prediction, 
               6 
               9 
             
             
               base-layer 
             
             
               Interlaced sequence, luma, 16 × 16 prediction, 
               12 
               17 
             
             
               enhancement-layer 
             
             
               Interlaced sequence, luma, 16 × 8 prediction, 
               12 
               9 
             
             
               enhancement-layer 
             
             
               Interlaced sequence, chroma, 8 × 8 prediction 
               3 
               9 
             
             
               Interlaced sequence, chroma, 8 × 4 prediction 
               3 
               5 
             
             
                 
             
           
        
       
     
   
     FIG. 3  shows the processing performed on the luma samples read from memory  206  by unit  208 . As shown in  FIG. 3 , the luma-processing portion of unit  208  comprises enhancement-layer decoder means  300 , enhancement-layer pixel reconstruction means  302 , DCT-based upsample means  304 , full-resolution block select means  306 , DCT-based downsample means  308  and two-layer output formation means  310 . These elements of enhanced MCU processing means  208  use the reduced-resolution blocks from I and P frames stored in memory  206  to form predictions for a decoded macroblock. 
   The above-described structure of  FIG. 3  performs computational processing of luma pixel values input to unit  208  from memory  206 . This computational process is described in detail in appendices B to G. Briefly, however, decoder  300  unpacks the input 128-bit words into 16 constituent 8-bit codewords. Decoder  300 , employing the computational processing described in appendix B, derives d 0 (x,y) as an output. Enhancement-layer pixel reconstruction means  302 , employing the computational processing described in appendix C, derives r 0 (x,y) as an output in response to both the d 1 (x,y) input to unit  208  and the d 0 (x,y) output from decoder  300 . DCT-based upsample means  304 , employing the computational processing described in appendix D, horizontally upsamples the r 0  (x,y) input to derive r(x,y) at full resolution. Full-resolution block select means  306 , employing the computational processing described in appendix E, uses r(x,y) to derive a full-resolution block of predictions p(x,y) as an output. DCT-based downsample means  308 , employing the computational processing described in appendix F, horizontally downsamples the p(x,y) input to derive q(x,y) at half horizontal resolution. The block q(x,y) is applied as an input to two-layer output formation means  310 , which employs the computational processing described in appendix G, to derive the outputs p 1 (x,y) and p 0 (x,y) provided by unit  208  to adders  205 B and  205 E shown in  FIG. 2 . Although the computational processing required for chroma predictions are not shown in  FIG. 3 , they are described in detail in appendix H. 
   Returning again to  FIG. 2 , a video signal comprising the base-layer pixels defining each of successive picture fields or frames is output from memory  206  and input to sample-rate converter  210  which derives a display video signal output. The display video signal output from unit  210  represents a PIP display image. By way of example, assume that the size of a PIP display is intended to occupy ⅓ of the horizontal dimension and ⅓ of the vertical dimension of the entire HD display size. If the original resolution of the HD bit-stream is 1920×1080 interlaced, then the PIP decoded frames (in which the number of pixels in the horizontal direction has been decimated by a factor of ¾) are 480×1080 interlaced. Assuming a 1920×1080 interlaced HD display, the displayed PIP frames should be 640×360 interlaced. Therefore, in this example, the decoded frames stored in memory must be scaled by sample-rate converter  210  by a factor of 4/3 in the horizontal direction and ⅓ in the vertical direction. 
   In a realized embodiment of the present invention, the extra capacity required in 1 memory for storage of the ½ resolution enhancement-layer in encoded form adds only 1.98 Mbits to the 17.8 Mbits required for storage of the ¼ resolution base-layer. Thus, the inclusion of an encoded ½ resolution enhancement-layer increases the needed storage capacity of the base and enhancement-layer decimated-pixel memory by a relatively small amount (i.e., only a little more than 11%) to 19.78 Mbits.