Abstract:
A method of losslessly compressing and encoding signals representing image information is claimed. A lossy compressed data file and a residual compressed data file are generated. When the lossy compressed data file and the residual compressed data file are combined, a lossless data file that is substantially identical to the original data file is created.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present Application for Patent is a divisional of patent application Ser. No. 12/181,608, entitled “APPARATUS AND METHOD FOR ENCODING DIGITAL IMAGE DATA IN A LOSSLESS MANNER” filed Jun. 29, 2008, pending, which is a continuation of patent application Ser. No. 10/180,828, entitled “APPARATUS AND METHOD FOR ENCODING DIGITAL IMAGE DATA IN A LOSSLESS MANNER” filed Jun. 26, 2002, now U.S. Pat. No. 7,483,581, which claims priority to Provisional Application No. 60/302,853 entitled “A SYSTEM AND METHOD FOR ENCODING DIGITAL IMAGE AND VIDEO DATA IN A LOSSLESS MANNER FOR ARCHIVAL PURPOSES (LOSSLESS ENCODER)” filed Jul. 2, 2001, all of which are assigned to the assignee hereof and hereby expressly incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     I. Field of the Invention 
     The present invention relates to image processing and compression. More specifically, the invention relates lossless encoding of video image and audio information in the frequency domain. 
     II. Description of the Related Art 
     Digital picture processing has a prominent position in the general discipline of digital signal processing. The importance of human visual perception has encouraged tremendous interest and advances in the art and science of digital picture processing. In the field of transmission and reception of video signals, such as those used for projecting films or movies, various improvements are being made to image compression techniques. Many of the current and proposed video systems make use of digital encoding techniques. Aspects of this field include image coding, image restoration, and image feature selection. Image coding represents the attempts to transmit pictures of digital communication channels in an efficient manner, making use of as few bits as possible to minimize the band width required, while at the same time, maintaining distortions within certain limits. Image restoration represents efforts to recover the true image of the object. The coded image being transmitted over a communication channel may have been distorted by various factors. Source of degradation may have arisen originally in creating the image from the object. Feature selection refers to the selection of certain attributes of the picture. Such attributes may be required in the recognition, classification, and decision in a wider context. 
     Digital encoding of video, such as that in digital cinema, is an area that benefits from improved image compression techniques. Digital image compression may be generally classified into two categories: loss-less and lossy methods. A loss-less image is recovered without any loss of information. A lossy method involves an irrecoverable loss of some information, depending upon the compression ratio, the quality of the compression algorithm, and the implementation of the algorithm. Generally, lossy compression approaches are considered to obtain the compression ratios desired for a cost-effective digital cinema approach. To achieve digital cinema quality levels, the compression approach should provide a visually loss-less level of performance. As such, although there is a mathematical loss of information as a result of the compression process, the image distortion caused by this loss should be imperceptible to a viewer under normal viewing conditions. 
     Existing digital image compression technologies have been developed for other applications, namely for television systems. Such technologies have made design compromises appropriate for the intended application, but do not meet the quality requirements needed for cinema presentation. 
     Digital cinema compression technology should provide the visual quality that a moviegoer has previously experienced. Ideally, the visual quality of digital cinema should attempt to exceed that of a high-quality release print film. At the same time, the compression technique should have high coding efficiency to be practical. As defined herein, coding efficiency refers to the bit rate needed for the compressed image quality to meet a certain qualitative level. Moreover, the system and coding technique should have built-in flexibility to accommodate different formats and should be cost effective; that is, a small-sized and efficient decoder or encoder process. 
     Many compression techniques available offer significant levels of compression, but result in a degradation of the quality of the video signal. Typically, techniques for transferring compressed information require the compressed information to be transferred at a constant bit rate. 
     One compression technique capable of offering significant levels of compression while preserving the desired level of quality for video signals utilizes adaptively sized blocks and sub-blocks of encoded Discrete Cosine Transform (DCT) coefficient data. This technique will hereinafter be referred to as the Adaptive Block Size Discrete Cosine Transform (ABSDCT) method. This technique is disclosed in U.S. Pat. No. 5,021,891, entitled “Adaptive Block Size Image Compression Method And System,” assigned to the assignee of the present invention and incorporated herein by reference. DCT techniques are also disclosed in U.S. Pat. No. 5,107,345, entitled “Adaptive Block Size Image Compression Method And System,” assigned to the assignee of the present invention and incorporated herein by reference. Further, the use of the ABSDCT technique in combination with a Differential Quadtree Transform technique is discussed in U.S. Pat. No. 5,452,104, entitled “Adaptive Block Size Image Compression Method And System,” also assigned to the assignee of the present invention and incorporated herein by reference. The systems disclosed in these patents utilize what is referred to as “intra-frame” encoding, where each frame of image data is encoded without regard to the content of any other frame. Using the ABSDCT technique, the achievable data rate may be reduced from around 1.5 billion bits per second to approximately 50 million bits per second without discernible degradation of the image quality. 
     The ABSDCT technique may be used to compress either a black and white or a color image or signal representing the image. The color input signal may be in a YIQ format, with Y being the luminance, or brightness, sample, and I and Q being the chrominance, or color, samples for each 4:4:4 or alternate format. Other known formats such as the YUV, YC b C r  or RGB formats may also be used. Because of the low spatial sensitivity of the eye to color, most research has shown that a sub-sample of the color components by a factor of four in the horizontal and vertical directions is reasonable. Accordingly, a video signal may be represented by four luminance samples and two chrominance samples. 
     Using ABSDCT, a video signal will generally be segmented into blocks of pixels for processing. For each block, the luminance and chrominance components are passed to a block size assignment element, or a block interleaver. For example, a 16×16 (pixel) block may be presented to the block interleaver, which orders or organizes the image samples within each 16×16 block to produce blocks and composite sub-blocks of data for discrete cosine transform (DCT) analysis. The DCT operator is one method of converting a time and spatial sampled signal to a frequency representation of the same signal. By converting to a frequency representation, the DCT techniques have been shown to allow for very high levels of compression, as quantizers can be designed to take advantage of the frequency distribution characteristics of an image. In a preferred embodiment, one 16×16 DCT is applied to a first ordering, four 8×8 DCTs are applied to a second ordering, 16 4×4 DCTs are applied to a third ordering, and 64 2×2 DCTs are applied to a fourth ordering. 
     The DCT operation reduces the spatial redundancy inherent in the video source. After the DCT is performed, most of the video signal energy tends to be concentrated in a few DCT coefficients. An additional transform, the Differential Quad-Tree Transform (DQT), may be used to reduce the redundancy among the DCT coefficients. 
     For the 16×16 block and each sub-block, the DCT coefficient values and the DQT value (if the DQT is used) are analyzed to determine the number of bits required to encode the block or sub-block. Then, the block or the combination of sub-blocks that requires the least number of bits to encode is chosen to represent the image segment. For example, two 8×8 sub-blocks, six 4×4 sub-blocks, and eight 2×2 sub-blocks may be chosen to represent the image segment. 
     The chosen block or combination of sub-blocks is then properly arranged in order into a 16×16 block. The DCT/DQT coefficient values may then undergo frequency weighting, quantization, and coding (such as variable length coding) in preparation for transmission. Although the ABSDCT technique described above performs remarkably well, it is computationally intensive. 
     Further, although use of the ABSDCT is visually lossless, it is sometimes desirable to recover data in the exact manner in which it was encoded. For example, mastering and archival purposes require to compress data in such a way as to be able to recover it exactly in its native domain. 
     Traditionally, a lossless compression system for images consists of a predictor, which estimates the value of the current pixel to be encoded. A residual pixel is obtained as the difference between the actual and the predicted pixel. The residual pixel is then entropy encoded and stored or transmitted. Since the prediction removes pixel correlation, the residual pixels have a reduced dynamic range with a characteristic two-sided exponential (Laplacian) distribution. Hence the compression. The amount of compression of the residuals depends on both the prediction and subsequent entropy encoding methods. Most commonly used prediction methods are differential pulse code modulation (DPCM) and its variants such as the adaptive DPCM (ADPCM). 
     A problem with pel-based prediction is that the residuals still have a high energy. It is due to the fact that only a small number of neighboring pixels are used in the prediction process. Therefore there is room to improve the coding efficiency of pel-based prediction schemes 
     SUMMARY OF THE INVENTION 
     Embodiments of the invention describe a system to encode digital image and video data in a lossless manner to achieve compression. The system is hybrid—meaning that it has a part that compresses the said data in a lossy manner and a part that compresses the residual data in a lossless fashion. For the lossy part, the system uses the adaptive block size discrete cosine transform (ABSDCT) algorithm. The ABSDCT system compresses the said data yielding a high visual quality and compression ratio. A residual image is obtained as the difference between the original and the decompressed one from the ABSDCT system. This residual is encoded losslessly using Golomb-Rice coding algorithm. Due to visually based adaptive block size and quantization of the DCT coefficients, the residuals have a very low energy, thus yielding good overall lossless compression ratios. 
     The ABSDCT system achieves a high compression ratio at cinema quality. Since it is block-based, it removes pixel correlation much better than any pel-based scheme. Therefore it is used as a predictor in the lossless system to be described here. In conjunction with this predictor a lossless encoding system is added to form a hybrid lossless compression system. It should be noted that the system is capable of compressing still images as well as motion images. If it is a still image, only the ABSDCT compressed data and entropy encoded residual data are used as the compressed output. For motion sequences, a decision is made whether to use intra-frame or inter-frame compression. For example, if f(t) represents an image frame at time instant t, F(t) and F(t+Δt) denote the DCTs of the image frames at time instants t and t+Δt, respectively. Note that Δt corresponds to the time interval between two consecutive frames. 
     The invention is embodied in an apparatus and method for compressing data that allows one to be able to recover the data in the exact manner in which the data was encoded. Embodiments comprise a system that performs intraframe coding, interframe coding, or a hybrid of the two. The system is a quality-based system that utilizes adaptively sized blocks and sub-blocks of Discrete Cosine Transform coefficient data. A block of pixel data is input to an encoder. The encoder comprises a block size assignment (BSA) element, which segments the input block of pixels for processing. The block size assignment is based on the variances of the input block and further subdivided blocks. In general, areas with larger variances are subdivided into smaller blocks, and areas with smaller variances are not be subdivided, provided the block and sub-block mean values fall into different predetermined ranges. Thus, first the variance threshold of a block is modified from its nominal value depending on its mean value, and then the variance of the block is compared with this threshold, and if the variance is greater than the threshold, then the block is subdivided. 
     The block size assignment is provided to a transform element, which transforms the pixel data into frequency domain data. The transform is performed only on the block and sub-blocks selected through block size assignment. For AC elements, the transform data then undergoes scaling through quantization and serialization. Quantization of the transform data is quantized based on an image quality metric, such as a scale factor that adjusts with respect to contrast, coefficient count, rate distortion, density of the block size assignments, and/or past scale factors. Serialization, such as zigzag scanning, is based on creating the longest possible run lengths of the same value. The stream of data is then coded by a variable length coder in preparation for transmission. Coding may be Huffman coding, or coding may be based on an exponential distribution, such as Golomb-Rice encoding. 
     The use of a hybrid compression system such as the ABSDCT, acts like a good predictor of pixel or DCT values. Therefore it results in a higher lossless compression ratio than the systems using pel-based prediction. The lossy portion provides digital cinema quality results—that is, the compression results in a file that is visually lossless. For the lossless portion, unlike Huffman codes, Golomb-Rice coding does not require any a priori code generation. Therefore, it does not require an extensive codebook to be stored as in Huffman coding. This results in an efficient use of the chip real estate. Hence, the chip size is reduced in hardware implementation. Further, the Golomb-Rice encoding is much simpler to implement than Huffman coding. Also, Golomb-Rice coding achieves a higher coding efficiency than the Huffman coding as the DCT coefficients or residuals have an exponential distribution naturally. Further, as the lossy portion of the compression system uses visually significant information in the block sub-division, context modeling is inherent in the residual encoding. This is important in that no extra storage registers are needed in gathering contextual data for the residual encoding. Since no motion estimation is used, the system is very simple to implement also. 
     An apparatus and method for losslessly compressing and encoding signals representing image information is claimed. Signals representing image information are compressed to create a compressed version of the image. The compressed version of the image is quantized, thereby creating a lossy version of the image. The compressed version of the image is also serialized to create a serialized quantized compressed version of the image. This version is then decompressed, and the differences between the original image and the decompressed version are determined, thereby creating a residual version of the image. The lossy version of the image and the residual version of the image may be output separately or combined, wherein the combination of the decompressed lossy version of the image and the residual version of the image is substantially the same as the original image. 
     A method of losslessly compressing and encoding signals representing image information is claimed. A lossy compressed data file and a residual compressed data file are generated. When the lossy compressed data file and the residual compressed data file are combined, a lossless data file that is substantially identical to the original data file is created. 
     Accordingly, it is an aspect of an embodiment to provide an apparatus and method to efficiently provide lossless compression. 
     It is another aspect of an embodiment that compresses digital image and audio information losslessly in a manner conducive to mastering and archival purposes. 
     It is another aspect of an embodiment to provide a lossless compression system on an interframe basis. 
     It is another aspect of an embodiment to provide a lossless compression system on an intraframe basis. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The features and advantages of the present invention will become more apparent from the detailed description set forth below when taken in conjunction with the drawings in which like reference characters identify correspondingly throughout and wherein: 
         FIG. 1  is a block diagram of an encoder portion of an image compression and processing system; 
         FIG. 2  is a block diagram of a decoder portion of an image compression and processing system; 
         FIG. 3  is a flow diagram illustrating the processing steps involved in variance based block size assignment; 
         FIG. 4   a  illustrates an exponential distribution of the Y component run-lengths in a DCT coefficient matrix; 
         FIG. 4   b  illustrates an exponential distribution of the C b  component run-lengths in a DCT coefficient matrix; 
         FIG. 4   c  illustrates an exponential distribution of the C r  component run-lengths in a DCT coefficient matrix; 
         FIG. 5   a  illustrates an exponential distribution of the amplitude size of the Y component or amplitude size of the Y component in a DCT coefficient matrix; 
         FIG. 5   b  illustrates an exponential distribution of the amplitude size of the C b  component or amplitude size of the C b  component in a DCT coefficient matrix; 
         FIG. 5   c  illustrates an exponential distribution of the amplitude size of the C r  component or amplitude size of the C r  component in a DCT coefficient matrix; 
         FIG. 6  illustrates a Golomb-Rice encoding process; 
         FIG. 7  illustrates an apparatus for Golomb-Rice encoding; 
         FIG. 8  illustrates a process of encoding DC component values; 
         FIG. 9  illustrates an apparatus for lossless compression; and 
         FIG. 10  illustrates a method of hybrid lossless compression. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In order to facilitate digital transmission of digital signals and enjoy the corresponding benefits, it is generally necessary to employ some form of signal compression. While achieving high compression in a resulting image, it is also important that high quality of the image be maintained. Furthermore, computational efficiency is desired for compact hardware implementation, which is important in many applications. 
     Before one embodiment of the invention is explained in detail, it is to be understood that the invention is not limited in its application to the details of the construction and the arrangement of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and are carried out in various ways. Also, it is understood that the phraseology and terminology used herein is for purpose of description and should not be regarded as limiting. 
     Image compression employed in an aspect of an embodiment is based on discrete cosine transform (DCT) techniques, such as that disclosed in co-pending U.S. Patent Application “Contrast Sensitive Variance Based Adaptive Block Size DCT Image Compression”, Ser. No. 09/436,085 filed on Nov. 8, 1999, assigned to the assignee of the present application and incorporated herein by reference. Image Compression and Decompression systems utilizing the DCT are described in co-pending U.S. Patent Application “Quality Based Image Compression”, Ser. No. 09/494,192, filed on Jan. 28, 2000, assigned to the assignee of the present application and incorporated herein by reference. Generally, an image to be processed in the digital domain is composed of pixel data divided into an array of non-overlapping blocks, N×N in size. A two-dimensional DCT may be performed on each block. The two-dimensional DCT is defined by the following relationship: 
                 X   ⁡     (     k   ,   l     )       =           α   ⁡     (   k   )       ⁢     β   ⁡     (   l   )             N   *   M         ⁢       ∑     m   =   0       N   -   1       ⁢           ⁢       ∑     n   =   0       N   -   1       ⁢           ⁢       x   ⁡     (     m   ,   n     )       ⁢     cos   ⁡     [         (       2   ⁢   m     +   1     )     ⁢   π   ⁢           ⁢   k       2   ⁢   N       ]       ⁢     cos   ⁡     [         (       2   ⁢   n     +   1     )     ⁢   π   ⁢           ⁢   l       2   ⁢   N       ]                 ,     0   ≦   k     ,     l   ≦     N   -   1             
where
 
               α   ⁡     (   k   )       ,       β   ⁡     (   k   )       =     {             1   ,       if   ⁢           ⁢   k     =   0                   2     ,       if   ⁢           ⁢   k     ≠   0             ,               
and
 
     x(m,n) is the pixel at location (m,n) within an N×M block, and 
     X(k,l) is the corresponding DCT coefficient. 
     Since pixel values are non-negative, the DCT component X(0,0) is always positive and usually has the most energy. In fact, for typical images, most of the transform energy is concentrated around the component X(0,0). This energy compaction property is what makes the DCT technique such an attractive compression method. 
     The image compression technique utilizes contrast adaptive coding to achieve further bit rate reduction. It has been observed that most natural images are made up of relatively slow varying flat areas, and busy areas such as object boundaries and high-contrast texture. Contrast adaptive coding schemes take advantage of this factor by assigning more bits to the busy areas and less bits to the less busy areas. 
     Contrast adaptive methods utilize intraframe coding (spatial processing) instead of interframe coding (spatio-temporal processing). Interframe coding inherently requires multiple frame buffers in addition to more complex processing circuits. In many applications, reduced complexity is needed for actual implementation. Intraframe coding is also useful in a situation that can make a spatio-temporal coding scheme break down and perform poorly. For example, 24 frame per second movies can fall into this category since the integration time, due to the mechanical shutter, is relatively short. The short integration time allows a higher degree of temporal aliasing. The assumption of frame-to-frame correlation breaks down for rapid motion as it becomes jerky. Intraframe coding is also easier to standardize when both 50 Hz and 60 Hz power line frequencies are involved. Television currently transmits signals at either 50 Hz or 60 Hz. The use of an intraframe scheme, being a digital approach, can adapt to both 50 Hz and 60 Hz operation, or even to 24 frame per second movies by trading off frame rate versus spatial resolution. 
     For image processing purposes, the DCT operation is performed on pixel data that is divided into an array of non-overlapping blocks. Note that although block sizes are discussed herein as being N×N in size, it is envisioned that various block sizes may be used. For example, a N×M block size may be utilized where both N and M are integers with M being either greater than or less than N. Another important aspect is that the block is divisible into at least one level of sub-blocks, such as N/i×N/i, N/i×N/j, N/i×M/j, and etc. where i and j are integers. Furthermore, the exemplary block size as discussed herein is a 16×16 pixel block with corresponding block and sub-blocks of DCT coefficients. It is further envisioned that various other integers such as both even or odd integer values may be used, e.g. 9×9. 
       FIGS. 1 and 2  illustrate an image processing system  100  incorporating the concept of configurable serializer. The image processing system  100  comprises an encoder  104  that compresses a received video signal. The compressed signal is transmitted using a transmission channel or a physical medium  108 , and received by a decoder  112 . The decoder  112  decodes the received encoded data into image samples, which may then be exhibited. 
     In general, an image is divided into blocks of pixels for processing. A color signal may be converted from RGB space to YC 1 C 2  space using a RGB to YC 1 C 2  converter  116 , where Y is the luminance, or brightness, component, and C 1  and C 2  are the chrominance, or color, components. Because of the low spatial sensitivity of the eye to color, many systems sub-sample the C 1  and C 2  components by a factor of four in the horizontal and vertical directions. However, the sub-sampling is not necessary. A full resolution image, known as 4:4:4 format, may be either very useful or necessary in some applications such as those referred to as covering “digital cinema.” Two possible YC 1 C 2  representations are, the YIQ representation and the YUV representation, both of which are well known in the art. It is also possible to employ a variation of the YUV representation known as YCbCr. This may be further broken into odd and even components. Accordingly, in an embodiment the representation Y-even, Y-odd, Cb-even, Cb-odd, Cr-even, Cr-odd is used. 
     In a preferred embodiment, each of the even and odd Y, Cb, and Cr components is processed without sub-sampling. Thus, an input of each of the six components of a 16×16 block of pixels is provided to the encoder  104 . For illustration purposes, the encoder  104  for the Y-even component is illustrated. Similar encoders are used for the Y-odd component, and even and odd Cb and Cr components. The encoder  104  comprises a block size assignment element  120 , which performs block size assignment in preparation for video compression. The block size assignment element  120  determines the block decomposition of the 16×16 block based on the perceptual characteristics of the image in the block. Block size assignment subdivides each 16×16 block into smaller blocks, such as 8×8, 4×4, and 2×2, in a quad-tree fashion depending on the activity within a 16×16 block. The block size assignment element  120  generates a quad-tree data, called the PQR data, whose length can be between 1 and 21 bits. Thus, if block size assignment determines that a 16×16 block is to be divided, the R bit of the PQR data is set and is followed by four additional bits of Q data corresponding to the four divided 8×8 blocks. If block size assignment determines that any of the 8×8 blocks is to be subdivided, then four additional bits of P data for each 8×8 block subdivided are added. 
     Referring now to  FIG. 3 , a flow diagram showing details of the operation of the block size assignment element  120  is provided. The variance of a block is used as a metric in the decision to subdivide a block. Beginning at step  202 , a 16×16 block of pixels is read. At step  204 , the variance, v16, of the 16×16 block is computed. The variance is computed as follows: 
             var   =         1     N   2       ⁢       ∑     i   =   0       N   -   1       ⁢           ⁢       ∑     j   =   0       N   -   1       ⁢           ⁢     x     i   ,   j     2           -       (       1     N   2       ⁢       ∑     i   =   0       N   -   1       ⁢           ⁢       ∑     j   =   0       N   -   1       ⁢           ⁢     x     i   ,   j             )     2             
where N=16, and x i,j  is the pixel in the i th  row, j th  column within the N×N block. At step  206 , first the variance threshold T16 is modified to provide a new threshold T′16 if the mean value of the block is between two predetermined values, then the block variance is compared against the new threshold, T′16.
 
     If the variance v16 is not greater than the threshold T16, then at step  208 , the starting address of the 16×16 block is written into temporary storage, and the R bit of the PQR data is set to 0 to indicate that the 16×16 block is not subdivided. The algorithm then reads the next 16×16 block of pixels. If the variance v16 is greater than the threshold T16, then at step  210 , the R bit of the PQR data is set to 1 to indicate that the 16×16 block is to be subdivided into four 8×8 blocks. 
     The four 8×8 blocks, i=1:4, are considered sequentially for further subdivision, as shown in step  212 . For each 8×8 block, the variance, v8 i , is computed, at step  214 . At step  216 , first the variance threshold T8 is modified to provide a new threshold T′8 if the mean value of the block is between two predetermined values, then the block variance is compared to this new threshold. 
     If the variance v8 i  is not greater than the threshold T8, then at step  218 , the starting address of the 8×8 block is written into temporary storage, and the corresponding Q bit, Q i , is set to 0. The next 8×8 block is then processed. If the variance v8 i  is greater than the threshold T8, then at step  220 , the corresponding Q bit, Q i , is set to 1 to indicate that the 8×8 block is to be subdivided into four 4×4 blocks. 
     The four 4×4 blocks, j i =1:4, are considered sequentially for further subdivision, as shown in step  222 . For each 4×4 block, the variance, v4 ij , is computed, at step  224 . At step  226 , first the variance threshold T4 is modified to provide a new threshold T′4 if the mean value of the block is between two predetermined values, then the block variance is compared to this new threshold. 
     If the variance v4 ij  is not greater than the threshold T4, then at step  228 , the address of the 4×4 block is written, and the corresponding P bit, P ij , is set to 0. The next 4×4 block is then processed. If the variance v4 ij  is greater than the threshold T4, then at step  230 , the corresponding P bit, P ij , is set to 1 to indicate that the 4×4 block is to be subdivided into four 2×2 blocks. In addition, the address of the 4 2×2 blocks are written into temporary storage. 
     The thresholds T16, T8, and T4 may be predetermined constants. This is known as the hard decision. Alternatively, an adaptive or soft decision may be implemented. For example, the soft decision varies the thresholds for the variances depending on the mean pixel value of the 2N×2N blocks, where N can be 8, 4, or 2. Thus, functions of the mean pixel values, may be used as the thresholds. 
     For purposes of illustration, consider the following example. Let the predetermined variance thresholds for the Y component be 50, 1100, and 880 for the 16×16, 8×8, and 4×4 blocks, respectively. In other words, T16=50, T8=1100, and T4=880. Let the range of mean values be 80 and 100. Suppose the computed variance for the 16×16 block is 60. Since 60 is greater than T16, and the mean value 90 is between 80 and 100, the 16×16 block is subdivided into four 8×8 sub-blocks. Suppose the computed variances for the 8×8 blocks are 1180, 935, 980, and 1210. Since two of the 8×8 blocks have variances that exceed T8, these two blocks are further subdivided to produce a total of eight 4×4 sub-blocks. Finally, suppose the variances of the eight 4×4 blocks are 620, 630, 670, 610, 590, 525, 930, and 690, with corresponding means values 90, 120, 110, 115. Since the mean value of the first 4×4 block falls in the range (80, 100), its threshold will be lowered to T′4=200 which is less than 880. So, this 4×4 block will be subdivided as well as the seventh 4×4 block. 
     Note that a similar procedure is used to assign block sizes for the luminance component Y-odd and the color components, C b  and C r . The color components may be decimated horizontally, vertically, or both. 
     Additionally, note that although block size assignment has been described as a top down approach, in which the largest block (16×16 in the present example) is evaluated first, a bottom up approach may instead be used. The bottom up approach will evaluate the smallest blocks (2×2 in the present example) first. 
     Referring back to  FIG. 1 , the PQR data, along with the addresses of the selected blocks, are provided to a DCT element  124 . The DCT element  124  uses the PQR data to perform discrete cosine transforms of the appropriate sizes on the selected blocks. Only the selected blocks need to undergo DCT processing. 
     The image processing system  100  also comprises DQT element  128  for reducing the redundancy among the DC coefficients of the DCTs. A DC coefficient is encountered at the top left corner of each DCT block. The DC coefficients are, in general, large compared to the AC coefficients. The discrepancy in sizes makes it difficult to design an efficient variable length coder. Accordingly, it is advantageous to reduce the redundancy among the DC coefficients. 
     The DQT element  128  performs 2-D DCTs on the DC coefficients, taken 2×2 at a time. Starting with 2×2 blocks within 4×4 blocks, a 2-D DCT is performed on the four DC coefficients. This 2×2 DCT is called the differential quad-tree transform, or DQT, of the four DC coefficients. Next, the DC coefficient of the DQT along with the three neighboring DC coefficients within an 8×8 block are used to compute the next level DQT. Finally, the DC coefficients of the four 8×8 blocks within a 16×16 block are used to compute the DQT. Thus, in a 16×16 block, there is one true DC coefficient and the rest are AC coefficients corresponding to the DCT and DQT. 
     The transform coefficients (both DCT and DQT) are provided to a quantizer for quantization. In a preferred embodiment, the DCT coefficients are quantized using frequency weighting masks (FWMs) and a quantization scale factor. A FWM is a table of frequency weights of the same dimensions as the block of input DCT coefficients. The frequency weights apply different weights to the different DCT coefficients. The weights are designed to emphasize the input samples having frequency content that the human visual or optical system is more sensitive to, and to de-emphasize samples having frequency content that the visual or optical system is less sensitive to. The weights may also be designed based on factors such as viewing distances, etc. 
     The weights are selected based on empirical data. A method for designing the weighting masks for 8×8 DCT coefficients is disclosed in ISO/IEC JTC1 CD 10918, “Digital compression and encoding of continuous-tone still images—part 1: Requirements and guidelines,” International Standards Organization, 1994, which is incorporated herein by reference. In general, two FWMs are designed, one for the luminance component and one for the chrominance components. The FWM tables for block sizes 2×2, 4×4 are obtained by decimation and 16×16 by interpolation of that for the 8×8 block. The scale factor controls the quality and bit rate of the quantized coefficients. 
     Thus, each DCT coefficient is quantized according to the relationship: 
                 DCT   q     ⁡     (     i   ,   j     )       =     ⌊         8   *     DCT   ⁡     (     i   ,   j     )             fwm   ⁡     (     i   ,   j     )       *   q       ±     1   2       ⌋           
where DCT(i,j) is the input DCT coefficient, fwm(i,j) is the frequency-weighting mask, q is the scale factor, and DCTq(i,j) is the quantized coefficient. Note that depending on the sign of the DCT coefficient, the first term inside the braces is rounded up or down. The DQT coefficients are also quantized using a suitable weighting mask. However, multiple tables or masks can be used, and applied to each of the Y, Cb, and Cr components.
 
     AC values are then separated  130  from DC values and processed separately. For DC elements, a first DC component value of each slice is encoded. Each subsequent DC component value of each slice is then represented as the difference between it and the DC component value preceding it, and encoded  134 . For lossless encoding, the initial DC component value of each slice and the differences are encoded  138  using Golomb-Rice, as described with respect to  FIGS. 6 and 8 . Use of Golomb-Rice encoding for the differences between successive DC component values is advantageous in that the differentials of the DC component values tend to have a two-sided exponential distribution. The data may then be temporarily stored using a buffer  142 , and then transferred or transmitted to the decoder  112  through the transmission channel  108 . 
       FIG. 8  illustrates a process of encoding DC component values. The process is equally applicable for still image, video image (such as, but not limited to, motion pictures or high-definition television) and audio. For a given slice of data  804 , a first DC component value of the slice is retrieved  808 . The first DC component value is then coded  812 . Unlike AC component values, the DC component values need not be quantized. In an embodiment, a single DC value for a 16×16 block is used regardless of the block size assignment breakdown. It is contemplated that any fixed sized block, such as 8×8 or 4×4, or any variable block size as defined by the block size assignment, may be used. The second, or next, DC component value of a given slice is then retrieved  816 . The second DC component value is then compared with the first DC component value, and the difference, or residual, is encoded  820 . Thus, the second DC component value need only be represented as the difference between it and the first value. This process is repeated for each DC component value of a slice. Thus, an inquiry  824  is made as to whether the end of the slice (last block and therefore last DC value) is reached. If not  828 , the next DC value of the slice is retrieved  816 , and the process repeats. If so  832 , the next slice is retrieved  804 , and the process repeats until all of the slices of a frame, and all of the frames of the file are processed. 
     An objective of lossless encoding of DC component values is to generate residual values that tend to have a low variance. In using DCTs, the DC coefficient component value contributes the maximum pixel energy. Therefore, by not quantizing the DC component values, the variance of the residuals is reduced. 
     For AC elements, the block of data and frequency weighting masks are then scaled by a quantizer  146 , or a scale factor element. Quantization of the DCT coefficients reduces a large number of them to zero which results in compression. In a preferred embodiment, there are 32 scale factors corresponding to average bit rates. Unlike other compression methods such as MPEG2, the average bit rate is controlled based on the quality of the processed image, instead of target bit rate and buffer status. 
     To increase compression further, the quantized coefficients are provided to a scan serializer  150 . The serializer  150  scans the blocks of quantized coefficients to produce a serialized stream of quantized coefficients. Zigzag scans, column scanning, or row scanning may be employed. A number of different zigzag scanning patterns, as well as patterns other than zigzag may also be chosen. A preferred technique employs 8×8 block sizes for the zigzag scanning. A zigzag scanning of the quantized coefficients improves the chances of encountering a large run of zero values. This zero run inherently has a decreasing probability, and may be efficiently encoded using Huffman codes. 
     The stream of serialized, quantized AC coefficients is provided to a variable length coder  154 . The AC component values may be encoded either using Huffman encoding or Golomb-Rice encoding. For DC component values, Golomb-Rice encoding is utilized. A run-length coder separates the coefficients between the zero from the non-zero coefficients, and is described in detail with respect to  FIG. 6 . In an embodiment, Golomb-Rice coding is utilized. Golomb-Rice encoding is efficient in coding non-negative integers with an exponential distribution. Using Golomb codes is more optimal for compression in providing shorter length codes for exponentially distributed variables. 
     In Golomb encoding run-lengths, Golomb codes are parameterized by a non-negative integer m. For example, given a parameter m, the Golomb coding of a positive integer n is represented by the quotient of n/m in unary code followed by the remainder represented by a modified binary code, which is └log 2  m┘ bits long if the remainder is less than or equal to 2 ┌log     2      m┐ −m, otherwise, ┌log 2  m┐ bits long. Golomb-Rice coding is a special case of Golomb coding where the parameter m is expressed as m=2 k . In such a case the quotient of n/m is obtained by shifting the binary representation of the integer n to the right by k bits, and the remainder of n/m is expressed by the least k bits of n. Thus, the Golomb-Rice code is the concatenation of the two. Golomb-Rice coding can be used to encode both positive and negative integers with a two-sided geometric (exponential) distribution as given by
 
 p   α ( x )= cα   |x|   (1)
 
     In (1), α is a parameter that characterizes the decay of the probability of x, and c is a normalization constant. Since p α (x) is monotonic, it can be seen that a sequence of integer values should satisfy
 
 p   α ( x   i =0)≧ p   α ( x   i =−1)≧ p   α ( x   i =+1)≧ p   α ( x   i =−2)≧ . . .   (2)
 
     As illustrated in  FIGS. 4   a ,  4   b ,  4   c  and  5   a ,  5   b ,  5   c , both the zero-runs and amplitudes in a quantized DCT coefficient matrix have exponential distributions. The distributions illustrated in these figures are based on data from real images.  FIG. 4   a  illustrates the Y component distribution  400  of zero run-lengths versus relative frequency. Similarly,  FIGS. 4   b  and  4   c  illustrates the Cb and Cr component distribution, of zero run-lengths versus relative frequency  410  and  420 , respectively.  FIG. 5   a  illustrates the Y component distribution  500  of amplitude size versus relative frequency. Similarly,  FIGS. 5   b  and  5   c  illustrates the Cb and Cr component distribution of amplitude size versus relative frequency,  510  and  520 , respectively. Note that in  FIGS. 5   a ,  5   b , and  5   c  the plots represent the distribution of the size of the DCT coefficients. Each size represents a range of coefficient values. For example, a size value of four has the range {−15,−14, . . . −8,8, . . . ,14,15}, a total of 16 values. Similarly, a size value of ten has the range {−1023,−1022, . . . , −512,512, . . . , 1022,1023}, a total of 1024 values. It is seen from  FIGS. 4   a ,  4   b ,  4   c ,  5   a ,  5   b  and  5   c  that both run-lengths and amplitude size have exponential distributions. The actual distribution of the amplitudes can be shown to fit the following equation (3): 
                       p   ⁡     (     X     k   ,   l       )       =           2   ⁢   λ       2     ⁢   exp   ⁢     {       -       2   ⁢   λ         ⁢          X     k   ,   l              }         ,   k   ,     l   ≠   0             (   3   )               
In (3), X k,l  represents the DCT coefficient corresponding to frequency k and l in the vertical and horizontal dimensions, respectively, and the mean
 
                 μ   x     =     1       2   ⁢   λ           ,         
variance
 
               σ   x   2     =       1     2   ⁢   λ       .           
Accordingly, the use of Golomb-Rice coding in the manner described is more optimal in processing data in DCTs.
 
     Although the following is described with respect to compression of image data, the embodiments are equally applicable to embodiments compressing audio data. In compressing image data, the image or video signal may be, for example, either in RGB, or YIQ, or YUV, or Y Cb Cr components with linear or log encoded pixel values. 
       FIG. 6  illustrates the process  600  of encoding zero and non-zero coefficients. As the DCT matrix is scanned, the zero and non-zero coefficients are processed separately and separated  604 . For zero data, the length of zero run is determined  608 . Note that run-lengths are positive integers. For example, if the run-length is found to be n, then a Golomb parameter m is determined  612 . In an embodiment, the Golomb parameter is determined as a function of the run length. In another embodiment, the Golomb parameter (m) is determined by the following equation (4)
 
 m= ┌log 2    n┐   (4)
 
     Optionally, the length of run-lengths and associated Golomb parameters are counted  616  by a counter or register. To encode the run length of zeros n, a quotient is encoded  620 . In an embodiment, the quotient is determined as a function of the run length of zeros and the Golomb parameter. In another embodiment, the quotient (Q) is determined by the following equation (5):
 
 Q=└n/ 2 m ┘  (5)
 
In an embodiment, the quotient Q is encoded in unary code, which requires Q+1 bits. Next, a remainder is encoded  624 . In an embodiment, the remainder is encoded as a function of the run length and the quotient. In another embodiment, the remainder (R) is determined using the following equation (6):
 
 R=n −2 m   Q   (6)
 
In an embodiment, the remainder R is encoded in an m-bit binary code. After, the quotient Q and the remainder R are determined, the codes for Q and R are concatenated  628  to represent an overall code for the run length of zeros n.
 
     Nonzero coefficients are also encoded using Golomb-Rice. Since the coefficient amplitude can be positive or negative, it is necessary to use a sign bit and to encode the absolute value of a given amplitude. Given the amplitude of the non-zero coefficient being x, the amplitude may be expressed as a function of the absolute value of the amplitude and the sign. Accordingly, the amplitude may be expressed as y using the following equation (7): 
     
       
         
           
             
               
                 
                   y 
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               2 
                               ⁢ 
                               x 
                             
                             , 
                             
                               
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                                 ⁢ 
                                 x 
                               
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                               0 
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 2 
                                 ⁢ 
                                 
                                    
                                   x 
                                    
                                 
                               
                               - 
                               1 
                             
                             , 
                             otherwise 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Accordingly, the value of a non-zero coefficient is optionally counted by a counter, or register,  632 . It is then determined  636  if the amplitude is greater than or equal to zero. If it is, the value is encoded  640  as twice the given value. If not, the value is encoded  644  as one less than twice the absolute value. It is contemplated that other mapping schemes may also be employed. The key is that an extra bit to distinguish the sign of the value is not needed. 
     Encoding amplitudes as expressed by equation (7) results in that positive values of x being even integers and negative values become odd integers. Further, this mapping preserves the probability assignment of x as in (2). An advantage of encoding as illustrated in equation (7) allows one to avoid using a sign bit to represent positive and negative numbers. After the mapping is done, y is encoded in the same manner as was done for the zero-run. The procedure is continued until all coefficients have been scanned in the current block. 
     It is important to recognize that although embodiments of the invention are determine values of coefficients and run lengths as a function of equations (1)-(7), the exact equations (1)-(7) need not be used. It is the exploitation of the exponential distribution of Golomb-Rice encoding and of DCT coefficients that allows for more efficient compression of image and audio data. 
     Since a zero-run after encoding is not distinguishable from a non-zero amplitude, it may be necessary to use a special prefix code of fixed length to mark the occurrence of the first zero-run. It is common to encounter all zeros in a block after a non-zero amplitude has been encountered. In such cases, it may be more efficient to use a code referring to end-of-block (EOB) code rather than Golomb-Rice code. The EOB code is again, optionally, a special fixed length code. 
     According to equation (1) or (3), the probability distribution of the amplitude or run-length in the DCT coefficient matrix is parameterized by α or λ. The implication is that the coding efficiency may be improved if the context under which a particular DCT coefficient block arises. An appropriate Golomb-Rice parameter to encode the quantity of interest may then be used. In an embodiment, counters or registers are used for each run-length and amplitude size value to compute the respective cumulative values and the corresponding number of times that such a value occurs. For example, if the register to store the cumulative value and number of elements accumulated are R rl  and N rl , respectively, the following equation (6) may be used as the Rice-Golomb parameter to encode the run-length: 
                   ⌈       log   2     ⁢       R   rl       N   rl         ⌉           (   6   )               
A similar procedure may be used for the amplitude.
 
     The residual pixels are generated by first decompressing the compressed data using the ABSDCT decoder, and then subtracting it from the original data. Smaller the residual dynamic range, higher is the compression. Since the compression is block-based, the residuals are also generated on a block basis. It is a well-known fact that the residual pixels have a two-sided exponential distribution, usually centered at zero. Since Golomb-Rice codes are more optimal for such data, a Golomb-Rice coding procedure is used to compress the residual data. However, no special codes are necessary, as there are no run-lengths to be encoded. Further, there is no need for an EOB code. Thus, the compressed data consists of two components. One is the component from the lossy compressor and the other is from the lossless compressor. 
     When encoding motion sequences one can benefit from exploiting the temporal correlation as well. In order to exploit fully the temporal correlation, pixel displacement is first estimated due to motion, and then a motion compensated prediction is performed to obtain residual pixels. As ABSDCT performs adaptive block size encoding, block size information may be alternatively used as a measure of displacement due to motion. As a further simplification, no scene change detection is used. Instead, for each frame in a sequence first the intra-frame compressed data is obtained. Then the difference between the current and previous frame DCTs, are generated on a block-by-block basis. This is described further by U.S. patent application Ser. No. 09/877,578, filed Jun. 7, 2001, which is incorporated by reference herein. These residuals in the DCT domain are encoded using both Huffman and Golomb-Rice coding procedures. The final compressed output then corresponds to the one that uses the minimum number of bits per frame. 
     The lossless compression algorithm is a hybrid scheme that lends itself well to repurposing and transcoding by stripping off the lossless portion. Thus, using ABSDCT maximizes pixel correlation in the spatial domain resulting in residual pixels having a lower variance than those used in prediction schemes. The lossy portion of the overall system permits the user to achieve the necessary quality and data rates for distribution purposes without having to resort to interframe processing, thereby eliminating related motion artifacts and significantly reducing implementation complexities. This is especially significant in programs being distributed for digital cinema applications, since the lossy portion of the compressed material requires a higher level of quality in its distribution. 
       FIG. 9  illustrates a hybrid lossless encoding apparatus  900 .  FIG. 10  illustrates a process that may be run on such an apparatus. Original digital information  904  resides on a storage device, or is transmitted. Many of the elements in  FIG. 9  are described in more detail with respect to  FIGS. 1 and 2 . Frames of data are sent to a compressor  908 , comprising a block size assignment element  912 , a DCT/DQT transform element  916 , and a quantizer  920 . After the DCT/DQT is performed on the data, the data is converted into the frequency domain. In one output  922 , the data is quantized by the quantizer  920  and transferred to an output  924 , which may comprises storage and/or switching. All of the above described processing is on an intraframe basis. 
     The quantizer output is also transferred to a decompressor  928 . The decompressor  928  undoes the process of the compressor, going through an inverse quantizer  932 , and an IDQT/IDCT  936 , along with knowledge of the PQR data as defined by the BSA. The result of the decompressor  940  is fed to a subtractor  944  where it is compared with the original. Subtractor  944  may be a variety of elements, such as a differencer, that computes residual pixels as the difference between the uncompressed and the compressed and decompressed pixels for each block. Additionally, the differencer may obtain the residuals in the DCT domain for each block for conditional interframe coding. The result  948  of the comparison between the decompressed data and the original is the pixel residual file. That is, the result  948  is indicative of the losses experienced by the data being compressed and uncompressed. Thus, the original data is equal to the output  922  in combination with the result  948 . The result  948  is then serialized  952  and Huffman and/or Golomb Rice encoder  956 , and provided as a second output  960 . The Huffman and/or Golomb Rice encoder  956  may be a type of entropy encoder that encodes residuals pixels using Golomb Rice coding. A decision is made whether to use intraframe or interframe based on the minimum bits for each frame. Use of Golomb Rice coding of the residuals leads to higher overall compression ratios of the system. 
     Thus, the lossless, interframe output is a combination, or hybrid of two sets of data, the lossy, high quality image file ( 922 , or A) and the residual file ( 960  or C). 
     Interframe coding may also be utilized. The output of the quantizer is transferred to a store  964 , along with knowledge of the BSA. Upon gathering of a frame&#39;s worth of data, a subtractor  966  compares the stored frame  964  with a next frame  968 . The difference results in a DCT residual  970 , which is then serialized and/or Golomb-Rice encoded  974 , providing a third output data set  976  to the output  924 . Thus, an interframe lossless file of B and C is compiled. Thus, either combination (A+C or B+C) may be chosen based on size considerations. Further, a purely intraframe output may be desirable for editing purposes. 
     Referring back to  FIG. 1 , the compressed image signal generated by the encoder  104  may be temporarily stored using a buffer  142 , and then transmitted to the decoder  112  using the transmission channel  108 . The transmission channel  108  may be a physical medium, such as a magnetic or optical storage device, or a wire-line or wireless conveyance process or apparatus. The PQR data, which contains the block size assignment information, is also provided to the decoder  112  ( FIG. 2 ). The decoder  112  comprises a buffer  164  and a variable length decoder  168 , which decodes the run-length values and the non-zero values. The variable length decoder  168  operates in a similar but opposite manner as that described in  FIG. 6 . 
     The output of the variable length decoder  168  is provided to an inverse serializer  172  that orders the coefficients according to the scan scheme employed. For example, if a mixture of zigzag scanning, vertical scanning, and horizontal scanning were used, the inverse serializer  172  would appropriately re-order the coefficients with the knowledge of the type of scanning employed. The inverse serializer  172  receives the PQR data to assist in proper ordering of the coefficients into a composite coefficient block. 
     The composite block is provided to an inverse quantizer  174 , for undoing the processing due to the use of the quantizer scale factor and the frequency weighting masks. 
     The coefficient block is then provided to an IDQT element  186 , followed by an IDCT element  190 , if the Differential Quad-tree transform had been applied. Otherwise, the coefficient block is provided directly to the IDCT element  190 . The IDQT element  186  and the IDCT element  190  inverse transform the coefficients to produce a block of pixel data. The pixel data may then have to be interpolated, converted to RGB form, and then stored for future display. 
       FIG. 7  illustrates an apparatus for Golomb-Rice encoding  700 . The apparatus in  FIG. 7  preferably implements a process as described with respect to  FIG. 6 . A determiner  704  determines a run length (n) and a Golomb parameter (m). Optionally, a counter or register  708  is used for each run-length and amplitude size value to compute the respective cumulative values and the corresponding number of times that such a value occurs. An encoder  712  encodes a quotient (Q) as a function of the run length and the Golomb parameter. The encoder  712  also encodes the remainder (R) as a function of the run length, Golomb parameter, and quotient. In an alternate embodiment, encoder  712  also encodes nonzero data as a function of the non-zero data value and the sign of the non-zero data value. A concatenator  716  is used to concatenate the Q value with the R value. 
     As examples, the various illustrative logical blocks, flowcharts, and steps described in connection with the embodiments disclosed herein may be implemented or performed in hardware or software with an application-specific integrated circuit (ASIC), a programmable logic device, discrete gate or transistor logic, discrete hardware components, such as, e.g., registers and FIFO, a processor executing a set of firmware instructions, any conventional programmable software and a processor, or any combination thereof. The processor may advantageously be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. The software could reside in RAM memory, flash memory, ROM memory, registers, hard disk, a removable disk, a CD-ROM, a DVD-ROM or any other form of storage medium known in the art. 
     The previous description of the preferred embodiments is provided to enable any person skilled in the art to make or use the present invention. The various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without the use of the inventive faculty. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein. 
     Other features and advantages of the invention are set forth in the following claims.