Abstract:
Method and system for lossless compression coding of a digitally represented image. The image is expressed as one or more blocks, each block having a sequence of pixels with binary pixel values. Within each block, a predictor index is chosen that predicts a pixel value as a linear combination of adjacent (actual) pixel values. The predicted and actual values are compared, and twice the predicted value is compared with the sum of the actual value and a maximum predicted value, to determine a value index, which is used to represent each pixel value in a block in compressed format. Use of the value index representation reduces the average number of bits needed to express each pixel value by an estimated 33-46 percent, reduces the time required for compression encoding by an estimated 4-6 percent, and reduces the time required for decompression by an estimated 49-61 percent. The compression ratios achieved by this coding approach compare favorably with, and sometimes improve upon, the compression achieved by several well known compression methods. Several processes in determination of the compressed values can be performed in parallel to increase throughput or to reduce processing time.

Description:
FIELD OF THE INVENTION  
         [0001]    This invention relates to selective compression of digital images.  
         BACKGROUND OF THE INVENTION  
         [0002]    Compression of digital images using lossless schemes is an integral part of a wide variety of applications that include medical imaging, remote sensing, printing, and computers. Recent advances in digital electronics and electromechanics have also helped employment of digital images widely. The algorithms for compression (or coding) of images have become sophisticated, spurred by the applications and standardization activities such as JPEG (“Digital Compression and Coding of Continuous Tone Images”, ISO Document No. 10918-1). The lossy version of JPEG, introduced around 1990, gained an enormous following in the industry due to its simplicity, public domain software, efforts by the Independent JPEG Group (IJPEG), and availability of inexpensive custom hardware (C-Cube Microsystems). The lossless counterpart did not gain significant acceptance, but provided momentum in diversified research activities.  
           [0003]    The primary approaches in lossless compression coding have used differential pulse code modulation (DPCM), followed by entropy coding of the residuals (W. Pennebaker and J. Mitchell, ( JPEG Still Image Compression Standard , Van Nostrand Reinhold, New York, 1993). Recently, schemes that utilize transforms or wavelets have also been investigated and have gained acceptance (A. Zandi et al, “CREW: Compression with reversible embedded wavelets”, Proc. of Data Compression Conference, March 1995, pp. 212-221; F. Sheng et al, “Lossy and lossless image compression using reversible integer wavelet transforms”, Proc. I.E.E.E., 1998, ______). However, the majority of the promising techniques have employed sophisticated DPCM and entropy coding techniques. These methods rely heavily on the statistical modeling of the data (source) (M. Weinberger et al, “On universal context modeling for lossless compression of gray scale images”, I.E.E.E. Trans. on Image Processing, 1996. Although such approaches have given excellent compression performance, they are cumbersome to implement and often inefficient as software programmable solutions implemented on digital signal processors (DSPs) or general purpose microprocessors. Efforts have been made to reduce the complexity of the statistical modeling portion in some of the best performing coders, CALIC (X. Wu et al, “Context-based, adaptive, lossless image coding”, I.E.E.E. Trans. on Communications, vol. 45, 1997, pp. 437-444), and LOCO (M. Weinberger et al, “LOCO-1: A low complexity, context-based lossless image compression algorithm”, Proc. of 1996 Data Compression Conference, 1996, pp. 140-149). Even with such efforts, the computational complexity is daunting. One primary reason for this is a context switch that occurs on a pixel boundary. This approach introduces several data dependent compute and control complexities in the encoder and the decoder.  
           [0004]    What is needed is an image compression approach that reduces the computational complexity but retains many of the attractive features of the most flexible compression approaches. Preferably, the approach should allow selective uses of lossless compression and lossy compression for different portions of the same image, without substantially increasing the complexity that is present when only lossless compression or only lossy compression is applied to an image.  
         SUMMARY OF THE INVENTION  
         [0005]    These needs are met by the invention, which provides a block-based coder that permits multiple levels of parallel implementation. The pixels in each input block are coded using a differential pulse code modulation (DPCM) scheme that uses one of several selectable predictors. The predictor for a block is chosen using local characteristics of the block to be coded. Prediction residuals (difference between actual and predicted values) are mapped to a non-negative integer scale and are coded using a new entropy-coded mechanism based on a modified Golomb Code (MGC). In addition, a novel run-length encoding scheme is used to encode specific patterns of zero runs. The invention permits parallel processing of data blocks and allows flexibility in ordering the blocks to be processed.  
           [0006]    A block of data values is examined to determine if the data values are all the same. A dc-only block uses a selected predictor and is easily compressed for later use. A non-dc-only block is examined according to selected criteria, and an optimal predictor is selected for this block. A residual value (actual value minus predicted value) is computed and clamped, and the block of clamped values and corresponding predictor index are processed for compression, using an efficient mapping that takes advantage of the full dynamic range of the clamped residual values.  
           [0007]    Context modeling can be included here without substantially increasing the computational complexity, by making the context switch granularity depend upon a “block” of pixels (e.g., P×Q), rather than on a single pixel, to allow inclusion of a transition region where a switch occurs. In some imaging applications, combinations of lossless and lossy techniques are combined to compress an image. For example, a portion of the image corresponding to a majority of text information might have to be losslessly coded, while the portion of the image with continuous-tone gray-scale information can be coded with some visual distortion to obtain higher compression. In such applications, the input image is segmented to identify the regions to be losslessly coded. Accordingly, lossy coders and lossless coders are switched on and off region-by-region. However, many of the lossy and lossless coders may work on entire images. The “chunking” by the segmentation algorithm makes it inefficient to code small blocks using the existing methods.  
           [0008]    The approach disclosed here is applicable to mixed mode images that may contain graphics, text, natural images, etc. The context switch at the block levels can be adapted for lossy coding. Thus, one obtains a single coder format that fits both lossy and lossless cases and encompasses an image segmenter as well. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]    [0009]FIGS. 1A, 1B,  1 C and  7  are schematic views of apparatus to practice the invention.  
         [0010]    [0010]FIGS. 2A, 2B and  2 C are a flow chart of the inventive procedure.  
         [0011]    [0011]FIG. 3 graphically illustrates zero-run statistics for an image.  
         [0012]    [0012]FIGS. 4, 5 and  6  illustrate use of parallelism with the invention.  
     
    
     DESCRIPTION OF THE INVENTION  
       [0013]    An image can be represented as a rectangular array of P×Q blocks of pixels, each of which may contain text, graphics, natural images, etc. The rectangular image to be coded is split into a multiple of P×Q blocks of images, where P and Q may, but need not, coincide. Each block is first evaluated to determine if all the pixels in the block have a selected value; this indicates a dc-only block. If all the pixel values in the block are identical, it is sufficient to code only one sample for that block. In addition, rather than encoding the raw pixel value, a prediction of the current sample value is made using previously coded adjacent sample values, and the difference between the current sample value and the predicted value is encoded. This technique, Differential Pulse Code Modulation (DPCM), has been used in image and speech coding.  
         [0014]    [0014]FIG. 1A is a block diagram of apparatus that can be used to practice the invention. An image can be represented as a rectangular block of P×Q blocks of pixels, each block having P rows and Q columns. Each block may contain text, graphics, natural images, etc. The image to be coded is split into a plurality of P×Q blocks of images. Rastrered pixel values are received in one or more streams by a raster-to-block converter  61  (optional) that converts rastered data to block data. A comparator  63  interrogates each block of pixel value data and determines if the data in a given block are all “dc”; that is, if all pixel values in the given block have the same value. If the comparator answers “yes”, a differential encoder  65  encodes dc differential data for that dc block(e.g., all values constant) and sends the compressed dc block data to a compressed data module  79  that accumulates compressed data for each block.  
         [0015]    For non-dc blocks, where the answer to the query of the comparator  63  is “no”, the optimal prediction scheme has the potential to vary block-by-block, or even pixel-by-pixel. A prediction scheme that is optimal for the current input block is chosen, block-by-block, from among several predictors. The different predictor schemes may be statically or dynamically chosen. A predictor selection module  67  receives the input block of pixel value differences, selects the optimal predictor for the current input block, and provides this information for a predictor module  69  and for the compressed data module  79 .  
         [0016]    Where static predictor selection is implemented, a set of predictors is selected to be used in a certain image coding system. For a given block, the predictor that is optimal for this block is chosen, and the information on which this selection is based is sent to a decoder as part of a coded bitstream. In a dynamic selection scheme, an optimal predictor for a given block can be found and used to obtain the prediction differences or residuals. The information needed to uniquely specify a predictor may be sent to the decoder as part of the coded bitstream.  
         [0017]    Let x(i,j) be the current pixel image value to be encoded, where the index i represents the scan line of the current pixel and the index j represents the pixel location on the scan line. For example, three neighboring sample values, x(i−1,j−1), x(i−1,j) and x(i,j−1) can be used to predict the value for the current sample. In this example, the prediction can be made as a linear combination 
           x   p ( i,j )= a·x ( i −1 ,j −1)+ b·x ( i −1 ,j )+ c·x ( i,j− 1),  (1) 
         [0018]    where the real numbers a, b and c characterize the predictor.  
         [0019]    In a static selection scheme, the predictor coefficients are restricted to a predetermined set. For example, static predictor coefficients may be restricted to eight linear combinations of the three known pixel image values, as illustrated in Table 1  
                                                           TABLE 1                           Predictor Coefficients                Predictor Index   a   b   c                            0   1   0   0           1   0   1   0           2   0   0   1           3   1   1   −1           4   1   0.5   −0.5           5   0.5   1   −0.5           6   −0.5   0.5   1           7   0.5   −0.5   1                      
 
         [0020]    In Table 1, the coefficients a, b and c for any predictor index Pred_index have an algebraic sum of 1 (not required). In a static prediction system, for each input block the predictor, among a fixed number of choices, such as eight in Table 1, the most suitable for the current input block is chosen, and this information is sent to the decoder as a three-bit index.  
         [0021]    In a dynamic selection scheme, the predictor coefficients can take any values and are not restricted to a fixed set of values for a given input block. The encoded values of the filter coefficients are also sent to the decoder.  
         [0022]    In the predictor module  69 , because the dynamic range of the input pixels is known for a block, the predicted values are arranged to lie in the same range. For example, each of the input samples with an M-bit representation has a value in the range [0, 2 M −1]. Depending upon the predictor coefficients used and the pixel values, the predicted value may lie outside the normal range of [0, 2 M −1]. As a result, the prediction values are preferably clamped to fall within the dynamic range of the input pixels.  
         [0023]    For example, where M=8 bits per pixel image are used to form the images, let a=b=1, c=−1, x(i,j−1)=x(i,j−1)=0 and x(i−1,j−1)=128. According to the prediction relation (1), the predicted value is x p (i,j)=−128. Because the predicted value x p (i,j) is less than the minimum value, the predicted value is clamped to the minimum value, x min , which is 0 here. In a similar manner, a predicted value greater than the maximum value is clamped to the maximum value, x max , which is 128 here.  
         [0024]    One clamping procedure that can be followed in this example is 
         if ( x   p ( i,j )&lt; x   min )  x   p ( i,j )= x   min ; 
         if ( x   p ( i,j )&gt; x   max )  x   p ( i,j )= x   max . 
         [0025]    Another procedure, expressed in mathematical form, that achieves this result is 
           x   p ( i,j ) clamped =min{max{ x   min   , x   p ( i,j )},  x   max }  (2A) 
         or 
           x   p ( i,j ) clamped =max{min{ x   max   , x   p ( i,j )},  x   min }.  (2B) 
         [0026]    A third mathematical procedure that achieves the desired result is 
           x   p ( i,j ) clamped =0.5 {|x   p ( i,j )− x   min   |−|x   p ( i,j )− x   max   |+x   max   −x   min },  (3) 
         [0027]    For each procedure, the values after clamping are limited to a range 
           x   min   ≦x   p ( i,j )≦ x   max ,  (4) 
         [0028]    where x min  may be 0 and x max  may be  2   M −1, if desired.  
         [0029]    A difference module  71  receives a block of actual pixel values x(i,j) and a corresponding block of predicted pixel values x p (i,j) and forms and issues difference values Δx(i,j)=x p (i,j)−x(i,j). These difference values are received by a block encoder  73  and by a variable length code (VLC) table selector  75 . The block encoder  73  forms and issues compressed data for non-dc blocks with the information from the VLC table selector  75 , which provides information on which VLC table should be used. A compressed data block module  79  concatenates all information from the different blocks and issues the compressed bitstream in a specific format.  
         [0030]    Where the following block is a dc-only block, the Pred_index number 0 is used. Where the following block is not dc-only, the predictor that gives the best cumulative results for each P×Q block is chosen. Thus, each P×Q block may require a different choice of Pred_index. Given a block to be encoded, any suitable criterion may be used to select the predictor coefficients. Specification of any of the eight possible predictors in Table 1 uses a three-bit field (for non-dc-only blocks). The number of predictor indices is not limited to 8 and may be any reasonable number.  
         [0031]    [0031]FIG. 1B is a block diagram illustrating an approach for implementing the encoder block  65  for a dc block of data. A mapper module  65 A receives an input signal, representing the dc value for that block, at a first input terminal and receives a selected dc prediction value for that block at a second input terminal. The mapper module  65 A provides a mapper output signal that is received at a first input terminal of a dc/modified Golomb coding (MGC) module  65 B. The dc/MGC module  65 B receives a (constant length) MGC vector K, discussed in the following, at a second input terminal. The MGC module  65 B provides an output bitstream of compressed (dc) block data that is received by the compressed data module  79  (FIG. 1A).  
         [0032]    [0032]FIG. 1C is a block diagram illustrating an approach for implementing the encoder block  73  for a non-dc block. A mapper module  73 A receives an input block of (non-constant) data x(i,j) at a first input terminal and receives difference data Δx(i,j) for that block at a second input terminal. The mapper module  73 A provides an output signal that is received at a first input terminal by a run-length modified Golomb coding (MGC) module  73 B. The MGC module  73 B receives an MGC vector K, discussed in the following, at a second input terminal. The MGC module  73 B provides an output bitstream of compressed (non-dc) block data that is received by the compressed data module  79  (FIG. 1A).  
         [0033]    The difference 
         Δ x ( i,j )= x ( i,j )− x   p ( i,j )  (5) 
         [0034]    between a pixel image value x(i,j) and the corresponding predictor value x p (i,j) has a value in a range between −(2 M −1) and +(2 M −1). However, if the prediction value x p (i,j) is known and satisfies a constraint such as (4), the difference value Δx can take only an eight-bit range around the Prediction value so that a 1-1 mapping can be constructed of the difference, Δx=x−x p , onto, for example, the integer set [0, 2 M −1].  
         [0035]    For any predictor, the difference Δx(i,j) between the actual value and a predicted value of pixel content will have a maximum value and a minimum value that are related by 
           x   max   −x   min =2 M −1,  (6) 
         [0036]    although the individual values for the maximum and minimum values may vary from on e pixel to another pixel. A suitable 1-1 mapping of the positive integers and the negative integers in the pixel value range onto a single segment of the positive integers, such as [0, 511], is defined by 
           F (0)=0,  (7A) 
           F (Δ x )=2 ·Δx −1 (Δ x =1, 2, 3, . . . , 2 M −1),  (7B) 
           F (Δ x )=2 ·|Δx | (Δ x =−(2 M −1), −(2 M −2), . . . , −2, −1).  (7C) 
         [0037]    For the range of difference values for the quantity Δx(i,j), a modified mapping, F(Δx;mod), is introduced that (1) includes all difference values that can be reached, (2) has a range limited to at most 2 M −1 consecutive values and (3) is also 1-1. The mapping F(Δx;mod) is defined differently for each realistic range of the difference value Δx. For example, assume that M=8 and that the maximum value and minimum value for the difference Δx for a particular pixel are +5 and −250, respectively, with all difference values between −250 and +5 being reachable by the difference Δx. The mapping F(Δx;mod) provides the following sequence of correspondences for this example:  
                                                                             Δx   →   F(Δx;mod)                                0       0       1       1       −1       2       2       3       −2       4       3       5       −3       6       4       7       −4       8       5       9       −5       10       6       11       −6       12       −7       13       −8       14            . . .                 −250       255                  
 
         [0038]    The correspondence defined by the mapping F(Δx;mod) takes account of the fact that the integers +6, +7, . . . , +255, −255, −254, −253, −252, −251 cannot appear in the legitimate values for the difference Δx and are thus invalid integers that can be deleted in the sequence of (only) valid integers in this sequence. When the invalid integers Δx=+6, +7, . . . , +255, −255, −254, −253, −252, −251 are deleted from the sequence of all integers in the range [−255, +255], the remaining 256 integers permit construction of the 1-1 mapping F(Δx;mod) set forth in the preceding. The particular mapping F(Δx;mod) will depend upon the particular maximum and minimum values for the difference Δx. Other suitable 1-1 mappings (permutations) that achieve the same result as the mapping F(Δx;mod) can also be used here. The mapping F(Δx;mod) can be generalized to other choices of the index M as well.  
         [0039]    Existence of a mapping such as F(Δx;mod) can be used to calculate the code word index of the differential value. The following computation procedure is used for a choice of M=8:  
                                                                       int getVldIndex //unsigned char prediction//           {           int levels, maxval, tmp;           unsigned int index;           int x, xh;                levels = 256;           maxval = levels − 1;           xh = prediction;           x = input;           tmp = 2*xh;           if ((x &lt;= xh) &amp;&amp; (tmp &lt;= (maxval + x))){           index = 2*(x − xh);           }           else if { (x &lt;= xh) &amp;&amp; (tmp &gt; maxval + x))){           index = maxval − x;           }           else if ((x &gt; xh) &amp;&amp; (tmp &lt; x)){           index = x;           }           else if { (x &gt; xh) &amp;&amp; (tmp &gt;= x)){           index = 2*(x − xh) − 1;           {                return index;           }                      
 
         [0040]    The procedure set forth in the preceding is illustrated in flow chart format in FIGS. 2A, 2B and  2 C. The system provides or receives a block of binary-valued numbers, including at least one Provided Value (“Prov Value”), in step  101 .  
         [0041]    In step  103 , the system determines if the pixel values in the present block all have the same value so that the block is a dc block. If the answer to the question in  103  is “yes”, the system chooses a selected dc predictor coefficient, such as Pred_index=0 in Table 1, in step  105 , and computes a Predicted Value (“Pred Value”) for the block values, using a dc predictor coefficient. From step  105 , the system moves to step  109 , discussed in the following. If the answer to the question in  103  is “no”, the system moves to step  107 , where it chooses a second Pred_index and a selected set of non-dc predictor coefficients and computes at least one Predicted Value in the block, using the non-dc predictor coefficients.  
         [0042]    In step  109  (optional), the system limits each predicted binary value to a selected range of values, with a max value. In step  111 , the system computes a Product Value (“Prod Value”), equal to twice the Predicted Value. In step  113 , the system computes a Difference Value, equal to the difference between the Provided Value and the corresponding Predicted Value.  
         [0043]    In step  115 , the system determines if both of (1) Provided Value≦Predicted Value and (2) Product Value≦Provided Value+max value are satisfied. If the answer to the compound question in  115  is “yes”, the system moves to step  117  and computes a Value Index, equal to twice the Difference Value, and moves to step  131 , discussed in the following.  
         [0044]    If the answer to the question in  115  is “no”, the system moves to step  119  and determines if both of (1) Provided Value≦Predicted Value and (2) Product Value&gt;Provided Value+max value are satisfied. If the answer to the compound question in  119  is “yes”, the system moves to step  121  and computes a Value Index, equal to max value minus the Provided Value, and moves to step  131 .  
         [0045]    If the answer to the question in  119  is “no”, the system moves to step  123  and determines if each of two conditions, (1) Provided Value&gt;Predicted Value and (2) Product Value&lt;Provided Value, is satisfied. If the answer to the compound question in  123  is “yes”, the system moves to step  125  and computes a Value Index, equal to the Provided Value, and moves to step  131 .  
         [0046]    If the answer to the question in  123  is “no”, the system moves to step  127  and determines if each of two conditions, (1) Provided Value&gt;Predicted Value and (2) Product Value≧Provided Value, is satisfied. If the answer to the compound question in  127  is “yes”, the system moves to step  129  and computes a Value Index, equal to twice the Difference Value minus 1, and moves to step  131 . In step  131 , the system uses the computed Value Index to represent at least one number in the block.  
         [0047]    Except for the boundary cases, where a pixel is located on an edge of a P×Q block, the positive difference values are scaled by a factor of 2, and then reduced by 1; the negative differential values are first negated (so that they become positive) and then multiplied by a factor of 2. The number 1 is subtracted from each scaled positive value (without negation) so that the result is odd-valued and can be distinguished from the scaled negative values, which correspond to even-values integers. For example, let x(i,j)=128 and the Prediction Value=130. Because the current image value x(i,j) is less than 130 and tmp (=2·130) is less than (255+128), the index is equal to 2·(130−128)=4.  
         [0048]    The residual or difference values Δx can be efficiently represented by entropy coding methods that use variable code lengths for each words. In the present coding scheme, a variable-length code word corresponding to the index computed as above is sent to the decoder as a part of the coded bitstream. The specific variable length code used here is a modified Golomb coding (MGC) technique as outlined in the following.  
         [0049]    Entropy coders based on Huffman coding have been widely used in the context of image and video coding. Although entropy coding provides a satisfactory result without requiring that extensive context analysis be performed, this approach requires provision of large tables for lookup operations and offers little flexibility for on-line adaptation. To address the lookup table size requirements, a Golomb coding method could be used, as set forth by S. Golomb in “Run-length encodings”, I.E.E.E. Trans. on Information Theory, vol. IT-12, 1966, pp. 399-401. However, Golomb codes can only be optimal for certain probability distributions. To alleviate this, an MGC technique was developed in a prior patent application, “Memory Efficient Variable Length Encoding and Decoding System”, U.S. Ser. No. 09/______. The MGC scheme uses a small table for adaptability and requires no table for actual decoding of the symbols. This scheme has the ability to optimally adapt to the varying statistical characteristics of the data, while requiring no tables for decoding of the symbols. The details are given in this patent application.  
         [0050]    The basic Golomb code is usually specified by a parameter m, preferably an integer greater than 1, for which a positive fraction p satisfies p m =0.5 (0.5&lt;p&lt;1). For any non-negative integer n, a variable-length code includes two parts: a variable length part, representing the integer portion of a ratio n/m, written [n/m] int , and a fixed-length part, n modulo m. To make the implementation simpler, m is often restricted to be a power of 2 (m=2 k  with k≧1), although this requirement can be relaxed. The fixed-length part (n mod m) is represented using k bits, where k is a selected integer satisfying 2 k−1 &lt;m≦2 k . The variable portion of the ratio n/m, written n′=[n/m] int , is represented using a run of n′ zeroes, followed by a 1. As a result, the bit length of any code word n is given by 
         bitLength( n )=[ n/m]   int   +k+ 1,  (8) 
         [0051]    where k (≈log 2 (m)) is the length of the fixed length portion of the representation. Although the implementation is simple, Golomb coding is not optimal for most probability distributions. The optimality is further compromised for values of m that are powers of two. The basic Golomb coding is improved by introducing the following modification.  
         [0052]    Let D be the set of all possible non-negative data fields. Divide D into N bins, 
           D=B 0∪ B 1 ∪ . . . ∪B ( N −1),  (9) 
         [0053]    where bin Bi has a selected number Mi of elements (Mi≧1). First assume that the number Mi is a power of two, expressed as 
         Mi=2 k(i) .  (10) 
         [0054]    If a data field (element) belongs to the bin Bi, the index within the bin can be uniquely identified using k(i) bits, where the bit length is 
         bitLength( Bi )= i +1 +k ( i ).  (11) 
         [0055]    A bin Bi is identified using runs of i zeroes followed by 1. Hence, A bin Bi can be represented using i+1 bits. This code can be uniquely specified by the vector K (given D) which is given by 
           K={k (0),  k (1), . . . ,  k ( N −1)}.  (12) 
         [0056]    To encode an input sample n, given the vector K, the following procedure can be followed:  
                                                                       prevIndex = 0;           index = 1 &lt;&lt; k(0);           bin = 0;           while (n &gt;= index)           {                bin = bin + 1;           prevIndex = index;           index = index + (1 &lt;&lt; k(bin));                }           encodeBin (bin);           encodeOffset(n − prevIndex);                      
 
         [0057]    where encodeBin is a procedure for encoding the variable length portion and encodeOffset is a procedure for encoding the fixed-length portion.  
         [0058]    One can easily verify that by changing the vector K, one will be able to adapt the variable-length codes according to the underlying probability distribution. This is the method used in this image coder.  
         [0059]    For example, the coder may use the following 16-entry table for varying values of K:  
                                           TABLE 2                           K-Vector Components.                Index   {k(0), k(1), k(2), k(3), k(4)}                            0   {6, 6, 6, 6, 6}           1   {5, 5, 5, 5, 5}           2   {4, 4, 4, 4, 4}           3   {3, 3, 3, 3, 3}           4   {2, 2, 2, 2, 2}           5   {1, 1, 1, 1, 1}           6   {2, 1, 1, 1, 2}           7   {0, 1, 1, 1, 1}           8   {5, 6, 6, 6, 6}           9   {4, 5, 5, 5, 5}           10   {3, 4, 4, 4, 4}           11   {2, 3, 3, 3, 3}           12   {2, 2, 1, 1, 2}           13   {2, 3, 3, 4, 4}           14   {0, 1, 2, 2, 3}           15   {0, 1, 2, 2, 2}                      
 
         [0060]    For code words with a bit-length greater than 17, an Escape coding technique is used. That is, the code word for ESCAPE is used, followed by an M-bit index representing the differential value between the input and the prediction. One constraint used here is k(i)=k(4) for i&gt;4. The quantity k(8) is preferably used for ESCAPE. While better choices may be available, this was chosen. One example of a variable-length code for ESCAPE is ‘000000001’. Another is ‘00000001’. In such an instance, all code words with more than 16 bit lengths greater than 16 are coded using an Escape coding techniqué.  
         [0061]    Several different MGC coding approaches can be used here, each with a different set of K-vector components, and a table need not have 16 entries. A suitable alternative to Table 2 is shown in Table 3, in which two K-vectors are changed relative to Table 2.  
                                           TABLE 3                           K-Vector Components.                Index   {k(0), k(1), k(2), k(3), k(4)}                            0   {6, 6, 6, 6, 6}           1   {5, 5, 5, 5, 5}           2   {4, 4, 4, 4, 4}           3   {3 ,3, 3, 3, 3}           4   {2, 2, 2, 2, 2}           5   {1, 1, 1, 1, 1}           6   {7, 7, 7, 7, 7}           7   {0, 1, 1, 1, 1}           8   {5, 6, 6, 6, 6}           9   {4, 5, 5, 5, 5}           10   {3, 4, 4, 4, 4}           11   {2, 3, 3, 3, 3}           12   {2, 2, 1, 1, 2}           13   {2, 3, 3, 4, 4}           14   {0, 1, 2, 2, 3}           15   {8, 8, 8, 8, 8}                      
 
         [0062]    The following example, with the choice M=8, may clarify the procedure. The coding includes the prescription  
         [0063]    x(i,j)=255, Prediction=20  
         [0064]    differential value=235  
         [0065]    vld index=255;  
         [0066]    Using the Modified Golomb Code (1,1,1,1,1), the number of elements in different bins is given by {2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, . . . }, and the code word-lengths corresponding to the elements in each bin is given by {2, 3, 4, 5, 6, 7, 8, 9, ESCAPE, 11, 12, 13, 14, 15, 16, 17, 18, . . . }. If raw coding is used, the vld-index 255 belongs to bin 127, and needs a total bit-length of 127+1+1 (to offset for ESCAPE)+1 (to uniquely represent the element in each bin) for a total of 130 bits. However, with ESCAPE coding, a nine-bit code to represent an ESCAPE code word, followed by an 8-bit code word to represent the vld-index 255, is sent (code word ‘00000000111111111’).  
         [0067]    Because the pixel values are differentially coded, the vld index value 0 is the most frequently occurring index value within a block. The zero-value index can be efficiently coded using the MGC table with k(0)=0. For typical images, consecutive zero-values indices, or zero-runs, are also common. For example, for a graphics image with block size P×Q=8×8, some zero-run statistics are shown in FIG. 3. It is clear that zero-runs of length 1 and length 8 are the most frequently occurring patterns in these images. For a more general block size, P×Q, the most frequently occurring patterns would be runs of lengths 1 and Q.  
         [0068]    To handle zero-runs in a manner similar to treatment of the number of vertical pixels in a P×Q block efficiently, zero-runs of length Q were checked only at row boundaries. For example, for an input block of 8×8 pixels, at most 8 zero-runs of length 8 are possible. If one or more zero-run of length Q is present, a bit is set to indicate the presence of this condition, followed by a P-bit codeword to specify which row of the P×Q block has the zero-run. For rows that do not contain a zero-run of length Q, the differential data are encoded using the MGC technique mentioned in the preceding. The c-code for this procedure is set forth in the following.  
                                                                                                                         lcount = 0;           for (i=0; i&lt;P; i++) { /* for each block line*/                rowz =0;           for (j=0; j&lt;Q; j++) {           rowz += (diff[i*Q=j] == 0);           }           ident[i] = (rowz==Q);           lcount += (rowz==Q);                }           if (lcount=0) {                putbits(1,1);                for (i=0; i&lt;P; i++)putbits(1,ident[i]);                }           else {                putbits(1,0);                }                      
 
         [0069]    The present invention has been compared with other lossless coders for encoding monochrome images in the JPEG-2000 image set, and the results are set forth in Table 4. LOCO and TCQ are two leading methods for image compression that achieve very high compression ratios. The LOCO method is discussed by M. Weinberger et al, ibid. The TCQ method is discussed by F. Sheng et al, ibid. The GZIP method is discussed By J. L., Gaily and M. Adler in “GZIP Documentation and Sources”, ftp://prep.ai.mit.edu/pub/gnv.  
         [0070]    All the images were monochrome quality, using an eight-bit representation for each pixel. The GZIP method, widely used in computer processing and based on the Lempel Ziv scheme, and its extensions were also applied to the set of images. The last column in Table 4, BALI, sets forth the results of the invention, for comparison. The BALI scheme provides compression ratios that are close to the LOCO and TCQ approaches for most images; and for one representative image, a target, BALI provides substantially greater compression ratios.  
                                         TABLE 4                           Bits/Pixel Required for Images In JPEG-2000 Set.                Image   LOCO   TCQ   GZIP   BALI                       woman   4.45   4.39   6.13   4.52           cafe   5.09   5.19   6.73   5.13           bicycle   4.36   4.41   5.73   4.34           target   2.19   2.13   1.08   1.56           aerial2   5.29   5.24   6.01   5.39                      
 
         [0071]    Another advantage of the invention arises from the possibility of parallel processing. Processing of data in blocks, use of the particular prediction schemes discussed herein and use of modified Golomb coding allows the system to process two or more blocks simultaneously, without requiring that each pixel value be processed seriatim and in a fixed order. This parallel processing approach provides a significant advantage in time required, in seconds, to compress and to decompress a given image.  
         [0072]    Coding of a given block of data according to the invention does not depend upon how any preceding block was coded. Thus, an image can be decomposed into an ordered sequence {R i } i  (i=0, 1, 2, . . . , L−1) of two or more regions, as illustrated in one approach in FIG. 4, and the regions can be coded in parallel. The only condition imposed on partitioning the image into two or more regions is that all blocks assigned to a region R i  should occur after all blocks in a preceding region assigned to a region R i-j  (j≧1) in the sequence, when a scan is performed in a left-to-right and top-to-bottom scanning order.(referred to herein as a scanning order pattern).  
         [0073]    One approach for performing this decomposition into regions is to split the image into multiple horizontal rows of blocks, where the individual regions R i  can be coded simultaneously using multiprocessing software or specialized hardware. Because the coding is performed in parallel, the processing of each block can be performed at a lower clock frequency, with lower power requirements, while maintaining high throughput. After the parallel coding is completed, the L processed (or compressed) bitstreams are merged in a straightforward operation, as illustrated in FIG. 5.  
         [0074]    A second level of parallelism is available by splitting an encoder into two sets of operations: (1) predictor selection and MGC index selection and (2) entropy coding. Each of these operations can be pipelined to further improve the computation performance.  
         [0075]    A third level of parallelism takes advantage of the fact that predictor selection and MGC selection involve similarly structured computations. Predictor selection, for example, requires that the residuals for different predictor choices be computed, using a common metric. Calculation of the metrics for different predictors can be done in parallel. A choice of the predictor with smallest residual is straightforward, after a metric is chosen.  
         [0076]    [0076]FIG. 6 illustrates an implementation of this level of parallelism. A block of pixel values is received at H different predictor analyzers, numbered h=0, 1, . . . , H−1, in a first step  151 . In step  153 , each predictor analyzer computes a corresponding prediction error residual values for all the pixels in the block. The errors for each of the H analyzers are pooled and compared in step  155 , using an appropriate error metric, such as sum of squares, or sum of absolute values, of the errors. The predictor with the lowest metric (including application of a tie breaker algorithm, if necessary) is chosen for the next stage or block, as part of step  155 . Each of the predictor analyzers can be operated independently and in parallel to maximize system performance and/or to minimize the time required for preparing a compressed image.  
         [0077]    The predictor calculations themselves indicate some degree of parallelism, with similar computations being performed for each pixel in the image. This parallelism can be exploited in a single instruction, multiple data (SIMD) approach as a sequence of software instructions or as a special hardware block. Use of SIMD instructions has become commonplace in microprocessors today; for example VIS on SPARC, MMX and SSE on x86, Altivec on PowerPC, MAX on PARISC, and 3DNow! on AMD, and on digital signal processors.  
         [0078]    [0078]FIG. 7 shows a block diagram of a general computer system  200 , which may be used to implement various hardware components of the invention, such as a client an applications server and a database management system. The computer system  200  includes a bus  208  or other communication mechanism for communicating information and a processor  210 , coupled with the bus  208 , for processing information. The computer system  200  also includes a main memory  212 , such as a random access memory (RAM) or other dynamic storage device, coupled to the bus  208 , for storing information and instructions to be executed by the processor  210 . The main memory  212  also may be used for storing temporary variables or other intermediate information during execution of instructions by the processor  210 . The computer system  200  further optionally includes read only memory (ROM)  214  or other static storage device, coupled to the bus  208 , for storing static information and instructions for the processor  210 . A storage device  216 , such as a magnetic disk or optical disk, is provided and is coupled to the bus  208  for storing information and instructions.  
         [0079]    The computer system  200  may also be coupled through the bus to a display  218 , such as a cathode ray tube (CRT), for displaying information to a computer user. An input device  220 , including alphanumeric and other keys, is coupled to the bus for communicating information and commands to the processor  210 . Another type of user input device is a cursor control  222 , such as a mouse, a trackball or cursor direction keys for communicating direction information and command selections to the processor  210  and for controlling cursor movement on the display  218 . This input device typically has one degree of freedom in each of two axes, such as x- and y-axes, that allows the device to specify locations in a plane.  
         [0080]    The functionality of the invention is provided by the computer system  200  in response to the processor  210  executing one or more sequences of instructions contained in main memory  212 . These instructions may be read into main memory  212  from another computer-readable medium, such as a storage device  216 . Execution of the sequences of instructions contained in the main memory  212  causes the processor  210  to perform the process steps described herein. In alternative embodiments, hard-wired circuitry may be used in place of, or in combination with, software instructions to implement the invention. Embodiments of the invention are not limited to any specific combination of hard-wired circuitry and software.  
         [0081]    The term “computer-readable medium”, as used herein, refers to any medium that participates in providing instructions to the processor  210  for execution. This medium may take many forms, including but not limited to non-volatile media, volatile media and transmission media. Non-volatile media includes, for example, optical and magnetic disks, such as the storage disks  216 . Volatile media includes dynamic memory  212 . Transmission media includes coaxial cables, copper wire and fiber optics and includes the wires that are part of the bus  208 . Transmission media can also take the form of acoustic or electromagnetic waves, such as those generated during radiowave, infrared and optical data communications.  
         [0082]    Common forms of computer-readable media include, for example, a floppy disk, a flexible disk, a hard disk, magnetic tape or any other magnetic medium, a CD-ROM, any other optical medium, punchcards, papertape, any other physical medium with patterns of holes or apertures, a RAM, a ROM, a PROM, an EPROM, a Flash-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can be read.  
         [0083]    Various forms of computer-readable media may be involved in carrying out one or more sequences of one or more instructions to the processor  210  for execution. For example, the instructions may initially be carried on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone, using a modem. A modem local to the computer system  200  can receive data over a telephone line and use infrared transmitter to convert and transmit the data to the an infrared detector connected to the computer system bus. The bus will carry the data to the main memory  212 , from which the processor receives and executes the instructions. Optionally, the instructions receive by the main memory  212  can be stored on the storage device  216 , either before or after execution by the processor  210 .  
         [0084]    The computer system  200  also includes a communications interface  224 , coupled to the bus  208 , which provides two-way data communication coupling to a network link  226  that is connected to a local area network (LAN) or to a wide area network (WAN). For example, the communications interface  224  may be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communications interface  224  may be a local area network card to provide a data communication connection to a compatible LAN. Wireless links may also be implemented. In any such implementation, the communications interface  224  sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.  
         [0085]    The network link  226  typically provides data communication through one or more networks to other data devices. For example, the data link  226  may provide a connection through an LAN  228  to a host computer  230  or to data equipment operated by an Internet Service Provider (ISP)  232 . The ISP, in turn, provides data communication services through the world wide packet data communication network, now commonly known as the “Internet”  234 , served by one or more servers  236 . The LAN  228  and the Internet  234  both use electrical, electromagnetic and/or optical signals to carry the digital data streams. The signals carried by these network, the signals carried on the network link  226  and the signals carried on the communications interface  224 , are examples of carrier waves that transport the information.