Abstract:
Lossless compression and the corresponding decompression of image and audio data are enabled using a combination of dynamic prediction and Golomb coding. First, data is converted from the RGB domain into the YUV domain. Next, a dynamic prediction algorithm is run to express pixel values as differential values rather than original bit values. Prediction coefficients are re-evaluated on the fly enabling additional compression because of more accurate predictors. An Adaptive Golomb Engine next performs an additional compression step, using an adaptive form of Golomb encoding in which mean values are variable across the data. The use of variable mean values reduces the deleterious effects found in conventional Golomb encoding in which localized regions of similar data are inefficiently coded if their bit values are uncommon in the data as a whole.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to compressing and decompressing audio and image data. In particular, the present invention relates to a lossless encoder that uses a dynamic predictor and adaptive Golomb encoder to compress audio and image data. 
     2. Description of the Related Art 
     The proliferation of digital content has created an associated need for media on which to store that digital content. To provide full-screen real-time animations, storage that is by today&#39;s standards quite sizeable in quantity must be available. For example, a typical high-definition image resolution is 1920 pixels by 1080 pixels, for a total of just under two megapixels. If the display is updated at 24 frames per second, this means that approximately 50 megapixels must be displayed every second. At a movie quality color depth of 48 bits per pixel, this means that 2.2 gigabits must be displayed every second, and a 90-minute movie requires almost 12 terabits (1.5 terabytes) of storage. Clearly, then, a way to compress these bits to save storage space is desirable. Unfortunately, conventional compression algorithms such as JPEG tend to be lossy—that is, information is lost as a part of the compression algorithm, and the original data cannot be completely recovered from the compressed data. This is an undesirable outcome, especially for videophiles and audiophiles not willing to sacrifice quality by giving up image resolution or audio fidelity. 
     What is needed, therefore, is a system and method for efficiently compressing image and audio data in a lossless manner. 
     SUMMARY OF THE INVENTION 
     The present invention enables the lossless compression and corresponding decompression of image and audio data using a combination of dynamic prediction and Golomb coding. A dynamic prediction algorithm is run to express pixel values as differential values rather than original bit values. Predictor coefficients are re-evaluated on the fly using a nonlinear feedback method, enabling additional compression because of more accurate predictions. An Adaptive Golomb Engine of the present invention next performs an additional compression step, using an adaptive form of Golomb encoding in which mean values are variable across the data. The use of variable mean values reduces the deleterious effects found in conventional Golomb encoding in which localized regions of similar data are inefficiently coded if their bit values are uncommon in the data as a whole. In addition, image data is first converted by the present invention from the RGB domain into a YUV domain before being processed by the dynamic prediction algorithm. 
     Because the compression performed by the Dynamic Predictor and the Adaptive Golomb Engine are lossless, application of the inverse compression logic in reverse order, that is, decompression using the Adaptive Golomb engine, followed by restoration of the original audio data or YUV image data by the Dynamic Predictor, and in the case of image data, ultimately performing an inverse transform to convert YUV image data to the RGB domain yields an identical set of data to that which was initially compressed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating a system in accordance with an embodiment of the present invention. 
         FIG. 2  is a flowchart illustrating a method for compressing a stream of data in accordance with an embodiment of the present invention. 
         FIG. 3  is a flowchart illustrating the operation of a Dynamic Predictor in accordance with an embodiment of the present invention. 
         FIG. 4  is a flowchart illustrating a method carried out by an Adaptive Golomb Engine in accordance with an embodiment of the present invention. 
         FIG. 5  is a flowchart illustrating a method for decompressing a stream of data in accordance with an embodiment of the present invention. 
     
    
    
     The figures depict preferred embodiments of the present invention for purposes of illustration only. One skilled in the art will readily recognize from the following discussion that alternative embodiments of the structures and methods illustrated herein may be employed without departing from the principles of the invention described herein. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       FIG. 1  illustrates a block diagram of a system in accordance with an embodiment of the present invention.  FIG. 1  includes a Pre-Processing Engine  102 , a Dynamic Predictor  104 , and an Adaptive Golomb Engine  106 . Also illustrated in  FIG. 1  are a data source  108 , and a composed stream  110 . 
     Data source  108  stores uncompressed image or audio data. Those of skill in the art will appreciate that data source  108 , although depicted as a single storage unit, may be one, two or many storage devices, as desired by the implementer. For example, where a full-length movie of several terabytes is to be compressed, it may exist in an uncompressed format across several different data sources. 
     Referring both to  FIG. 1  and  FIG. 2 , the uncompressed data from data source  108  is transmitted to system  100  and received  202  by Pre-Processing Engine  102 . If the data includes  203  color image or stereo sound data, Pre-Processing Engine  102  transforms  204  the data in a manner as described below. After the data has been transformed by Pre-Processing Engine  102 , if applicable, or else after it is received  202 , it is passed to Dynamic Predictor  104 . Dynamic Predictor  104  performs  206  a lossless encoding of the data as described below with respect to  FIG. 3 , and passes the compressed data to Adaptive Golomb Engine  106 . Adaptive Golomb Engine  106  performs  208  still another level of compression, as described below with respect to  FIG. 4 , and outputs  210  a compressed stream of data. Composed stream  110  can then be output to a storage device, transmitted to a remote location, etc. 
     Pre-Processing Engine 
     As noted above, image and audio data sought to be compressed is first pre-processed by Pre-Processing Engine  102 . In the case of image data, in a preferred embodiment, each pixel in the uncompressed image data includes values for three color channels—red (R), green (G) and blue (B). Pre-Processing Engine  102  preferably algebraically transforms the values for each pixel from the RGB domain into a YUV domain. This is a lossless transform that removes redundancy between channels. Although the Y channel may have higher entropy (average pixel values) than the original channels, the U and V channels preferably have smaller entropy, thus encoding more easily. In one embodiment the transform is of the following form: 
     
       
         
           
             Y 
             = 
             
               floor 
               ( 
               
                 
                   R 
                   + 
                   
                     2 
                     ⁢ 
                     G 
                   
                   + 
                   B 
                 
                 4 
               
               ) 
             
           
         
       
       
      
       U=B−G  
      
       
      
       V=R−G  
      
     
     As will be appreciated by those of skill in the art, the above transformations are completely invertible, resulting in no lost data. In the YUV domain, Y represents intensity, or “luminance,” while U and V represent chrominance values. Transforming RGB data into YUV data allows for better compression, since most of the image data is moved into a single channel—in this case the Y channel. Those of skill in the art will appreciate that there are other transformations for YUV that enjoy lossless invertability. 
     Similarly, for an audio stream having a left (L) and right (R) channel, 
     
       
         
           
             U 
             = 
             
               floor 
               ( 
               
                 
                   L 
                   + 
                   R 
                 
                 2 
               
               ) 
             
           
         
       
       
      
       V=L−R  
      
     
     Here, since the L and R channels are expected to be somewhat similar, V will be a fairly small number, which improves the overall compression operation. 
     Those of skill in the art will appreciate that other transforms can also be used. For example, in an alternative embodiment, 
     
       
         
           
             U 
             = 
             
               floor 
               ( 
               
                 
                   
                     7 
                     ⁢ 
                     L 
                   
                   + 
                   R 
                 
                 8 
               
               ) 
             
           
         
       
       
      
       V=L−R  
      
     
     which is also an invertible lossless transformation. In general, in the audio case, transforms of the form 
     
       
         
           
             U 
             = 
             
               floor 
               ( 
               
                 
                   aL 
                   + 
                   
                     
                       ( 
                       
                         b 
                         - 
                         a 
                       
                       ) 
                     
                     ⁢ 
                     R 
                   
                 
                 b 
               
               ) 
             
           
         
       
       
      
       V=L−R  
      
     
     often prove useful. 
     Once transformed by Pre-Processing Engine  102 , the data stream is then passed to Dynamic Predictor  104 . 
     Dynamic Predictor 
     In a preferred embodiment, DP  104  creates an approximately Laplacian statistic 
                 (     1     2   ⁢   λ       )     ·     exp   ⁡     (       -        Δ          /   λ     )         ,         
via nonlinear feedback on a predictor function P, for presentation to the Adaptive Golomb Engine  106 . DP  104  proceeds as follows.
 
     DP  104  can dynamically modify the predictor function P deterministically, according to local statistics of the previous Δ n . Conventional methods of prediction use, for example, optimized coefficients in the P algebra. But such methods typically involve storage of optimal coefficients in the compression stream. Instead, DP  104  allows the predictor function characteristics to percolate deterministically, on the basis only of known initial conditions. To later decompress the data, DP  104  can again precisely mimic this percolation. 
     Let the input data be denoted x=(x 0 , x 1 , . . . ) where each x i  is an integer. For example, for 16-bit monaural sound, one may have x i  ε[−2 15 ,2 15 −1], whereas for images one may have a luminance channel y with y i  ε[0, 255]. Then one considers an integer-valued predictor function
 
 P   n   =P ( x   n−1   ,x   n−2   , . . . , x   n−M )
 
     where M is a fixed “order,” which is used as a guess on the next datum x n . One forms the difference
 
Δ n   =x   n   −P   n ,
 
and sends the transformed data (Δ n ) to an entropy encoder. Those of skill in the art will recognize that for an order-1 predictor P:=x n−1  this simply requires compressing the first differences Δ n =x n −x n−1 . Preferably, the general datum Δ n  is “small,” in this way attempting compression. Losslessness is guaranteed because the coefficient of x n  is unity. That is, values for the first M data x 0 , . . . , x M−1  are stored, along with the ensuing Δ n  for n≧M. Decompression uses the recovered Δ n  to causally and losslessly construct
 
 x   n =Δ n   +P   n ( x   n−1 , . . . , x n−M ).
 
     Consider an analog input of at least slightly-correlated noise, according to the model recursion
 
 x   n   =rx   n−1 +ε n−1 ,
 
where r is a correlation constant, ε n  is an independent and identically distributed (i.i.d.) noise signal of variance ε 2  and zero mean (e.g. a Gaussian variable uncorrelated to anything else except itself), and normalized so that &lt;x n   2 &gt;=1=r 2 +ε 2 . Note that for r=1, ε=0 and the data x n  are all the same constant, while for r=0, uncorrelated noise x n =ε n  of unit variance. Note also that &lt;x n x n−1 &gt;=r, so that r is indeed a measure of inter-data correlation. The first-difference predictor P n =x n−1  has variance
 
&lt;Δ n   2 &gt;=&lt;( x   n   −x   n−1 ) 2 &gt;=1+1−2&lt; x   n   x   n−1 &gt;=2−2 r,  
 
and 2−2r may or may not be less than the direct variance &lt;x n   2 &gt;=1.
 
     This leads to the conclusion that for the correlated-noise model x n =rx n−1 +ε n−1 , encoding of first-difference data Δ n =x n −x n−1  is more efficient than direct encoding of the x n  if and only if r&gt;½. 
     A general form for order-M predictors is as follows: 
                 P   n     =           a   1     ⁢     x     n   -   1         +       a   2     ⁢     x     n   -   2         +     ⋯   ⁢           ⁢     a   M     ⁢     x     n   -   M           =       ∑     i   =   1     M     ⁢       a   i     ⁢     x     n   -   1               ,     
     ⁢   where                   ∑     i   =   1     M     ⁢     a   i       =   1.         
This normalization condition ensures that a constant input x n =c yields a zero difference Δ n =x n −P n . Next, we find a coefficient a such that the 2nd-order predictor function (M=2)
   P   n   =ax   n−1 +(1− a ) x   n−2    
results in minimum variance of the difference
 Δ n   =x   n   −P   n . 
     We proceed from
 
Δ n   =x   n   −ax   n−1 −(1− a ) x   n−2  
 
to calculate
 
&lt;Δ n   2 &gt;=1+ a   2 +(1− a ) 2 −2 ar− 2(1− a ) r   2 +2 a (1− a ) r.  
 
This quadratic form is minimized for a=(1+r)/2, whence
 
     
       
         
           
             
               
                 〈 
                 
                   Δ 
                   2 
                 
                 〉 
               
               min 
             
             = 
             
               
                 1 
                 2 
               
               ⁢ 
               
                 ( 
                 
                   1 
                   - 
                   
                     r 
                     2 
                   
                 
                 ) 
               
               ⁢ 
               
                 
                   ( 
                   
                     3 
                     - 
                     r 
                   
                   ) 
                 
                 . 
               
             
           
         
       
     
     Thus, the best (minimal variance) M=2 predictor for the noise model has 
                 Δ   n     =       x   n     -         1   +   r     2     ⁢     x     n   -   1         -         1   -   r     2     ⁢     x     n   -   2             ,         
and this variance performs better than a direct-encoding variance 1 when r exceeds about 0.4608. If the correlation r is not known ahead of time, or if r changes effectively with index n (time or space), then such calculations lose meaning.
 
     As noted above, DP  104  involves the use of dynamically modified coefficients. If the coefficients are made index-dependent, that is we allow a i →a i,n , the difference signal is 
                 Δ   n     =       x   n     -       ∑     i   =   1     M     ⁢       a     i   ,   n       ⁢     x     n   -   1               ,         
and a i,n  can be modified according to previous Δ values. Let us also force
 
                 a     M   ,   n       =     1   -       ∑     i   =   1       M   -   1       ⁢     a     i   ,   n             ,         
so that the normalization is guaranteed with just M−1 coefficients. In one embodiment, a nonlinear-feedback formula amounts to a prescription for incrementing/decrementing coefficient values by
   a   i,n+1   +=δ·sign (Δ n )· sign ( x   n−i   −x   n ), 
where δ is a (typically small) positive number, and sign(z):=1,0,−1 as z is positive, zero, negative, respectively. This adjustment of coefficients is a nonlinear process, and furthermore depends on past data. Using the sign of the previous Δ and the overall multiple of a given a i,n , Δ n  is generally forced toward zero.
 
     In one embodiment in order to improve speed performance, shift-rational arithmetic can be used by assuming δ=1 and 
                   Δ   n     =       x   n     -     (       (       ∑     i   =   1     M     ⁢       a     i   ,   n       ⁢     x     n   -   1           )     &gt;&gt;   s     )         ,     ⁢                 
which implies δ≈½ s . High speed can be achieved with the pure-integer arithmetic involved, and additionally, the integer coefficients a i,n  are merely incremented/decremented by 1 (or unchanged).
 
     Referring now to  FIG. 3 , there is shown a flowchart illustrating an algorithm for providing non-linear feedback to the Dynamic Predictor  104 . First, DP  104  chooses  302  an order M. Order M is preferably chosen by the implementer, and can vary according to experimental results. In one embodiment, the order is 16. Once the order has been chosen  302 , the coefficients (a 1,M , a 2,M , . . . , a M−1,M ) are initialized  304 . Note also that a M,M  is 1 minus the sum of the remaining coefficients. Next, DP  104  chooses  306  a shift amount s as described above. The order, shift and initial coefficients are then sent  308  to the output stream, as well as the data (x 0 , . . . , x M−1 ) itself  310 . Note that the data may be uncompressed data, or may already have been partially compressed by another algorithm, so long as it was a lossless algorithm. 
     Finally, if  312  there are more data to be read, (that is, n≧M), Δ n  is determined for each n, and sent  314  to the output stream. The coefficients are then updated  316  such that a i,n+1  is updated for each i ε[1,M−1], with δ=1. 
     Note that DP  104  preferably uses a 2-dimensional generalization of the predictor equation presented earlier when processing images; namely, for pixel values (x m,n ) at coordinates (m, n) we compute a difference 
                 Δ     m   ,   n       =       x     m   ,   n       -       ∑     i   ,   j       ⁢       A     i   ,   j       ⁢     x       m   -   i     ,     n   -   j                 ,         
where now we allow any lexicographically causal sum. For example, index pairs (i,j)=(0,−1), (−1,0), (−1,−1) can all have nonvanishing A i,j  in the classical sense of propagating the predictor algebra lexicographically. The feedback calculus of DP  104  is similarly generalized, so that the A i,j  are modified dynamically as one scans an image.
 
Adaptive Golomb Engine
 
     The compressed image stream output from Dynamic Predictor  104  is then provided as input to Adaptive Golomb Engine  106 . A Golomb encoder is an efficient way to represent data having a Laplacian distribution, such as the data output from Dynamic Predictor  104 . Data encoded using a Golomb encoder typically has a format including both unary and binary components. 
     As is known in the art, Golomb coding involves representing the most frequently-occurring values using tokens having a small number of bits. This results in a form of compression, since the tokens generally will have fewer bits than the pixel values they replace. However, there can exist areas of an image in which there are a series of values having a magnitude very different from the most frequently-occurring values, and yet which repeat often within the local region. For example, if the pixel value “230” is not common overall in the image data, it will likely not be a value selected for large savings using a small token. However, it may be the case that there is a region of the image with many values of or near “230”, even though the region is not large compared with the rest of the image. A conventional Golomb coding scheme sacrifices the extra bits used to repeat these values in order to achieve an overall satisfactory compression level. That is, if a token of fewer bits were used to express “230”, more bits would be required for a different token, and the overall compression rate would decrease. 
     System  100  improves upon this conventional method using Adaptive Golomb Engine  106  in coordination with Dynamic Predictor  104 . Adaptive Golomb Engine (AG)  106  determines how many bits to use for a token based on a region more localized than the overall image. AG  106  determines a mean, which is preferably a weighted average of the most recent values encountered by the AG  106 . For example, in one embodiment the previous ten values are considered. Because the mean is a moving average, if recent values have been close to, say, “230”, then the mean will trend toward “230”. On the other hand, if recent values have been closer to another value, e.g., “3”, then the mean will trend toward “3”. Because the mean is not fixed for an entire set of data, AG  106  therefore is able to achieve an optimal level of compression on a more local level than is achieved using non-adaptive Golomb coding. 
       FIG. 4  illustrates a flow chart of the operation of Adaptive Golomb Engine  106 . First, AG  106  sets ( 402 ) its mean to an initial value, which is preferably derived empirically. For example, in one embodiment the mean is 3. Next, AG  106  applies ( 404 ) the Golomb coding as described above to a pixel to be encoded. If ( 406 ) more pixels remain, then the mean is updated ( 408 ) to reflect a moving average of the most recent pixels, and the next pixel is encoded ( 410 ) using the updated mean. Once no more data ( 406 ) remains, the AG process terminates and outputs the stream of compressed data. 
     The compression performed by the Dynamic Predictor and the Adaptive Golomb Engine are lossless. Therefore, application of the inverse compression logic in reverse order, and, for image data, performing an inverse transform to convert YUV data back into the RGB domain yields an identical set of data to that which was initially compressed. Composed stream  110  is input into the Adaptive Golomb Engine  106  to be decompressed according to a decompression algorithm. 
     Referring now to  FIG. 5 , when AG  106  receives  502  a stream  110  to be decoded, it applies  504  an Adaptive Golomb decoding algorithm by using the initial mean to decipher the first encoded entry. From the mean and the deciphered first entry, AG  106  can then proceed to calculate a new mean and decode the next entry. In such a manner, the stream is decoded to be identical to the data before it was originally compressed by AG  106 . 
     When DP  104  receives a stream from AG  106  to be decompressed, it decodes  506  the compressed data by traversing each channel of the image, reconstructing original values from the stored differences and updating the coefficients exactly as they were updated during encoding. 
     Finally, once DP  104  has finished decoding the stream, if  507  it is color image or stereo sound data it is now in the YUV domain as transformed by the Pre-Processing Engine  102 . By applying the reverse transformation to each pixel or audio bit value, the value is transformed  508  from the YUV domain back into the original domain, yielding the original uncompressed image or audio data. Alternatively, if the data is not color image or stereo sound data, it need not be transformed as it is already now uncompressed. 
     The present invention has been described in particular detail with respect to a limited number of embodiments. Those of skill in the art will appreciate that the invention may additionally be practiced in other embodiments. First, the particular naming of the components, capitalization of terms, the attributes, data structures, or any other programming or structural aspect is not mandatory or significant, and the mechanisms that implement the invention or its features may have different names, formats, or protocols. Further, the system may be implemented via a combination of hardware and software, as described, or entirely in hardware elements. Also, the particular division of functionality between the various system components described herein is merely exemplary, and not mandatory; functions performed by a single system component may instead be performed by multiple components, and functions performed by multiple components may instead be performed by a single component. For example, the particular functions of the Dynamic Predictor  104 , Adaptive Golomb Engine  106 , and so forth may be provided in many or one module. 
     Some portions of the above description present the feature of the present invention in terms of algorithms and symbolic representations of operations on information. These algorithmic descriptions and representations are the means used by those skilled in the audio and graphics compression arts to most effectively convey the substance of their work to others skilled in the art. These operations, while described functionally or logically, are understood to be implemented by computer programs or hardware. Furthermore, it has also proven convenient at times, to refer to these arrangements of operations as modules or code devices, without loss of generality. 
     It should be borne in mind, however, that all of these and similar terms are to be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities. Unless specifically stated otherwise as apparent from the present discussion, it is appreciated that throughout the description, discussions utilizing terms such as “processing” or “computing” or “determining” or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system memories or registers or other such information storage, transmission or display devices. 
     Certain aspects of the present invention include process steps and instructions described herein in the form of an algorithm. It should be noted that the process steps and instructions of the present invention could be embodied in software, firmware or hardware, and when embodied in software, could be downloaded to reside on and be operated from different platforms used by real time network operating systems. 
     The present invention also relates to an apparatus for performing the operations herein. This apparatus may be specially constructed for the required purposes, or it may comprise a general-purpose computer selectively activated or reconfigured by a computer program stored in the computer. Such a computer program may be stored in a computer readable storage medium, such as, but not limited to, any type of disk including floppy disks, optical disks, CD-ROMs, magnetic-optical disks, read-only memories (ROMs), random access memories (RAMs), EPROMs, EEPROMs, magnetic or optical cards, application specific integrated circuits (ASICs), or any type of media suitable for storing electronic instructions, and each coupled to a computer system bus. Furthermore, the computers referred to in the specification may include a single processor or may be architectures employing multiple processor designs for increased computing capability. 
     The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Various general-purpose systems may also be used with programs in accordance with the teachings herein, or it may prove convenient to construct a more specialized apparatus to perform the required method steps. The required structure for a variety of these systems will appear from the description above. In addition, the present invention is not described with reference to any particular programming language. It is appreciated that a variety of programming languages may be used to implement the teachings of the present invention as described herein, and any references to specific languages are provided for disclosure of enablement and best mode of the present invention. 
     Finally, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes, and may not have been selected to delineate or circumscribe the inventive subject matter. Accordingly, the disclosure of the present invention is intended to be illustrative, but not limiting, of the scope of the invention.