Lossy Compression of Color Mosaic Images

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           Lossy Compression of Color Mosaic Images
                                                 Stephanie Kwan and Karen Zhu

                                                                     demosaicking on the compressed mosaic image later. Two
   Abstract—“Raw” color mosaic images produced by consumer           different approaches will be explored and compared with
digital cameras pose interesting lossy compression problems.         conventional       demosaicking-first,      compression-later
Conventionally, “raw” color mosaic images are first demosaicked      approaches.
and color-balanced, before being compressed for storage or
transmission. However, the new compression-first demosaicking-
                                                                        In the next section, the conventional demosaicking-first,
later approach has attracted much attention due to its efficiency.   compression-later approaches are outlined and serve as
This paper presents two lossy compression methods for                reference points for the new compression-first, demosicking-
compression-first demosaicking-later approach. The resulting         later approaches. In section III, existing compression-first
reconstructed images are compared with the ones compressed           demosaicking-later designs are discussed in brief. Section IV
using the conventional methods. It is shown that the proposed        introduces our new approaches to this problem and discusses
methods have much advantage over the conventional methods.
                                                                     the algorithms in detail. Experimental setup is given in
                                                                     section V, while results and analysis are given in section VI.
                       I. INTRODUCTION                               Finally, suggestions for future works are outlined in section
M      OST digital cameras are equipped with sensors that can
       only detect the intensity but not the frequency of
incoming light. A color filter array (CFA) is placed in front of
                                                                     II. THE CONVENTIONAL DEMOSAICKNG-FIRST COMPRESSION-
                                                                                      LATER APPROACHES
the light sensors to enable the intensity information of one
                                                                        Conventionally, the “raw” mosaic image data is first
color component, commonly red, green, or blue to be
                                                                     interpolated with a demosaicking algorithm, followed by a
recorded. The resulting image contains samples of these three
                                                                     color balancing scheme to obtain a continuous tone color
primary colors, interleaved in a two-dimensional (2-D) grid,
                                                                     RGB image. Then, a compression scheme is applied to reduce
or color mosaic pattern. The most commonly used CFA
                                                                     the size of the image for transmission or storage. To view the
pattern is the Bayer pattern (Fig. 1). To obtain the true
                                                                     compressed image, a matching decompression scheme is
continuous tone color image from the mosaic image, a process
                                                                     applied, and then the image is displayed. Fig. 2 below
called color-demosaicking is used to estimate the value of the
                                                                     illustrates this process with the RGB image compressed using
other two colors at the same pixel [1].
                                                                     a lossy compression scheme.

                                                                                                                                 RGB image
                                                                     Raw mosaic            Demosaic              Balance

                                                                     Compressed                                   storage        Lossy
                        Fig. 1. Bayer Pattern                        RGB image             Decompression                       Compression
   With limited storage space and processing power in digital
camera, image data compression is a key component for                Fig. 2. Conventional compression scheme for “raw” mosaic image.
digital cameras design. Conventionally, the “raw” mosaic
image is first interpolated with a demosaicking algorithm, and          In order to use the path illustrated in Fig. 2 as the reference
then compressed for storage. Since the demosaicking process          for comparison with the two new approaches later discussed
does not increase the information content of the original            in section IV, two specific lossy compression methods are
image, but only introduce redundant data, performing                 used and implemented.
compression after demosaicking is no more efficient then                1) RGB Compression: The RGB image obtained after color
performing compression directly on the “raw” mosaic image.           balancing is split into three separate channels. Each channel,
In fact, performing compression after demosaicking usually           red, green, and blue, is compressed independently using 5/3
introduces longer processing time and larger storage                 wavelet transform [3] and coded with the SPIHT algorithm
requirement [2].                                                     [4]. Bit allocation is performed such that the distortion of each
   The goal of this paper is to explore the scheme of lossily        channel is set to an equal value.
compressing “raw” mosaic image first, and performing                    2) YCrCb Compression: The RGB image obtained after

color balancing is transformed into the YCrCb color space.                     wavelet transform is then proposed for doing compression
The luminance and the chrominance channels are then                            directly on mosaic image without de-interleaving the RGB
compressed independently using 5/3 wavelet transform and                       components. Excellent results have been shown using this
coded with the SPIHT algorithm.                                                approach.
  To evaluate the quality of the compression methods,                             The reason behind the good performance of wavelet
Composite Peak Signal to Noise Ratio (CPSNR) is used.                          transform on “raw” color mosaic image is discussed in detail
                                                                               in [1]. The basic idea is that the four subbands generated by
  III. EXISTING COMPRESSION-FIRST DEMOSAICKING-LATER                           one level wavelet decomposition have clear connections to the
                                  SCHEMES                                      Bayer Pattern mosaic image. For example, applying the 2D
  In contrast to the conventional approach, the compression-                   low-pass filter of the 5/3 wavelet transform to the Bayer
first demosaicking-later approach directly compresses the                      mosaic image, the LL band can be interpreted as the
“raw” mosaic image. The basic idea of this approach is                         luminance channel of the full color image. On the other hand,
outlined in Fig. 3 below.                                                      the 2D 5/3 high-pass filter has the effect of spectral
                                                                               decorrelation. The HH subband resulted thus contains the
  Raw mosaic
                                                                mosaic image   details of the green channel and a highly smoothed color
                    Compression           Decompression
    Image                                                           Y’         difference signal.
                                                                                  The results presented in [1] are very interesting since it
                                                                               suggests that interleaved compression performs as well as the
                      Compressed             Color            Demosaic         deinterleaved compression, if not better. However, Zhang and
                      RGB image             Balance
                                                                               Wu [1] only focused on the lossless compression of the raw
  Fig. 3. Compression-first demosaicking-later scheme for “raw” mosaic
                                                                               mosaic image, while in real life lossy compression is more
image.                                                                         often required. In the next section, two lossy compression
                                                                               schemes based on the lossless approaches suggested in [1] are
  There are a number of literatures in this area, each using a                 proposed.
different compression method. They can be roughly
categorized into two groups: ones that separate the “raw”                              IV. PROPOSED LOSSY COMPRESSION SCHEME
mosaic image into RGB or YCrCb sub-channels for                                  In this section we propose two methods for lossily
compression, and ones that do not separate the “raw” mosaic
                                                                               compressing color mosaic images, the deinterleaved approach
image, but compress it directly. The terms deinterleaved and
                                                                               and the interleaved approach.
interleaved will be used to represent these two groups
respectively.                                                                    A. Deinterleaved Lossy Compression
  A. Deinterleaved Compression                                                    As illustrated in Fig. 4, the (square 2N x 2N) “raw” mosaic
   Most of the early works in the area of mosaic image                         image is first separated into three subimages. Each subimage
compression used deinterleaved compression. Tsai [2]                           only contains one of three colors, namely red, green, or blue.
proposed a scheme of separating the “raw” mosaic image into                    The approach used to separate the “raw” mosaic image into
the three color groups, red, green, and blue, and compress                     the red, green, and blue subimages are the same as the
each group separately with adaptive discrete cosine transform                  approach used in [3], and is outlined below.
(ADCT). Xie et al. [5] and Koh et al. [6] not only separated                      The red and blue subimages are created by simply merging
the “raw” image data into RGB groups, they also transformed                    neighboring pixels of the same color to form square
the RGB groups into the YCrCb groups. After that, Xie et al.                   subimages that has a size of N x N.
[5] compressed each group with JPEG-LS, while Koh et al.
[6] compress each group using JPEG baseline. Recently,                              B0, 0    G0,1   B0, 2   G0,3     B0, 4    G0,5     B0, 6    G0, 7
Zhang and Wu [1] have compared the above approaches by                              G1, 0    R1,1   G1, 2   R1,3     G1, 4    R1,5     G1, 6    R1, 7
applying both JPEG-LS and JPEG2000 compression on
                                                                                    B2, 0    G2,1 B2, 2     G2 , 3   B2, 4    G2 , 5   B2, 6    G2 , 7
separate RGB groups, and concluded that JPEG-LS, which
uses Differential Pulse Code Modulation (DPCM) coding,                              G3, 0    R3,1 G3, 2     R3,3     G3, 4    R3,5     G3,6     R3,7
performs better then JPEG2000, which uses wavelet                                   B4, 0    G4,1 B4, 2     G4 , 3   B4, 4    G4 , 5   B4, 6    G4 , 7
                                                                                    G5, 0    R5,1 G5, 2     R5,3     G5, 4    R5,5     G5,6     R5, 7
  B. Interleaved Compression                                                        B6, 0    G6,1 B6, 2     G6,3     B6, 4    G6,5     B6, 6    G6, 7
   In addition to deinterleaved compression, Zhang and Wu
                                                                                    G7 , 0   R7 ,1 G7 , 2   R7 ,3    G7 , 4   R7 ,5    G7 , 6   R7, 7
[1] also explored methods for doing interleaved compression.
They first observed that JPEG2000 out performs JPEG-LS
when applied to interleaved “raw” mosaic image data, proving
that wavelet decomposition has much advantage over DPCM
on interleaved color pixels. A unique so-called Mallat packet

   Sub-image R                                       Sub-image B
    R1,1        R1,3        R1,5        R1,7         B0,0     B0, 2    B0, 4    B0,6
                                                                                                Raw                                              Wavelet
    R3,1        R3,3        R3,5        R3,7         B2,0     B2, 2    B2, 4    B2,6         mosaic image            Separate into 3            Transform
                                                                                                  Y                  subimages R, G, B         (5/3 wavelet)      Lossy
    R5,1        R5,3        R5,5        R5,7         B4,0     B4, 2    B4, 4    B4,6                                                                           Compression
    R7 ,1       R7 ,3       R7 ,5       R7 ,7        B6,0     B6, 2    B6, 4    B6,6         Combine subimages                                 SPHITE +Arithmetic
                                                                                            back to mosaic pattern                                 Encoding
   The green pixels are arranged in a quincunx pattern. If we
simply shift the columns of green pixels by 1 pixel, and merge
the green pixels into a rectangular structure, a lot of false high                                    +                          Inverse Wavelet      SPHITE + Arithmetic
                                                                                               Color Balancing                      Transform              Decoding
frequencies will be created. Therefore, first, we create an                                                                        (5/3 wavelet)
image that has the same size as the original image, but only
contains the green components. Locations where pixels are
                                                                                              Final RGB image
non-green are set to 0.                                                                              X2’

         0          G0,1         0          G0 , 3    0       G0,5      0       G0 , 7     Fig. 4. Deinterleaved compression process of color mosaic image.

        G1, 0        0          G1, 2        0       G1, 4     0       G1, 6     0
            0       G2,1            0       G2, 3      0      G2 , 5     0      G2, 7      B. Interleaved Lossy Compression
        G3, 0           0       G3, 2           0    G3, 4      0      G3 , 6     0         Fig. 5 illustrates the process of performing lossy
                                                                                         compression directly on the interleaved color mosaic image.
         0          G4,1         0          G4, 3     0       G4 , 5    0       G4, 7
                                                                                         This approach is significantly simpler then the previous one
        G5, 0        0          G5 , 2       0       G5, 4     0       G5 , 6    0       due to the fact that the “raw” mosaic image is not separated
            0       G6,1            0       G6 , 3     0      G6 , 5     0      G6 , 7   into three subimages, but compressed directly. The mosaic
        G7 , 0          0       G7 , 2          0    G7 , 4     0      G7 , 6     0      image is lossily compressed using the same scheme used in
                                                                                         Deinterleaved Lossy Compression mentioned previously. It is
                                                                                         transformed using the Mallet packet wavelet transform, and
  This image is then passed through a low-pass filter H to                               lossily compressed using SPHITE, together with an arithmetic
avoid the generation of unwanted high frequencies.                                       coder. Fig. 6 shows the “raw” color mosaic image of
                              ⎡0 0 1 ⎤                                                   “isochart” image, and Fig. 7 shows a five level Mallet packet
                        H = ⎢0 2 4⎥
                                       ⎥                                                 wavelet decomposition of it.
                              ⎢0 0 1 ⎥
                              ⎣        ⎦
   This lowpass-filtered green subimage is then subsampled
(2:1) to keep the number of data points the same, and at the                                 mosaic image                   Wavelet            SPHITE +Arithmetic
same time transform the green subimage into a 2N x N                                              Y                        Transform               Encoding
                                                                                                                          (5/3 wavelet)
rectangular array.
   Since the Mallet packet wavelet transform takes in square                                                                          Lossy Compression

images, we first do a 1D wavelet transform on the rectangular
green subimage to separate the image into 2 subbands, each                                     mosaic image              Inverse Wavelet        SPHITE + Arithmetic
                                                                                                   Y’                       Transform
which is a square of N x N. Then for each of these subbands,                                                               (5/3 wavelet)
we perform Mallet packet wavelet transform and the
subsequent compression in the same manner as the red and                                                                                 Decompression
blue subimages.                                                                                      +
   To reconstruct the compressed color mosaic image,                                          Color Balancing

arithmetic and SPHIT decoding is first performed on the three
separate subimages, followed by inverse Mallet packet
                                                                                               Final RGB image
transform with inverse 5/3 wavelet. The three subimages are                                           X2’
then combined to form a close approximation of the original
“raw” mosaic image. At this point, the color mosaic image                                Fig. 5. Interleaved compression process of color mosaic image.
obtained can be compared with the original raw mosaic image
to evaluate the Peak Signal to Noise Ratio (PSNR) that results
from the compression process.
   The last step is to perform demosaicking and color
balancing on the processed color mosaic to display a normal
continuous tone RGB color image.

                                                                     to green rather than red or blue, attempts have been made to
                                                                     distribute distortions unequally in the subimages to see if an
                                                                     unequal distribution of distortion would result in images of
                                                                     better visual quality. We tried constraining the distortion ratio
                                                                     of R:G:B = 1:2:1, 2:1:2 as well as 1:3:1. Among these ratios,
                                                                     R:G:B ratio of 2:1:2 and R:G:B ratio of 1:1:1 give the best
                                                                       D. Comparison Schemes
                                                                       Three types of comparison are carried out in our experiment
                                                                     to show different aspects of this investigation.
                                                                        1) CPSNR comparison of Conventional approaches: As
                                                                     outlined in section II, two methods are implemented the
                                                                     conventional approach, namely the RGB compression scheme
                                                                     and the YCrCb compression scheme. Referring to Fig. 2, the
  Fig. 6. “raw” color mosaic image of Isochart.                      RGB image X before the lossy compression block and the
                                                                     RGB image X1’ after the decompression block are compared.
                                                                     The CPSNR between these two images is calculated using
                                                                     equation (1). The corresponding compression ratio is also
                                                                     calculated from the bitrate needed to code X1’.

                                                                                        ⎛                                           ⎞
                                                                                        ⎜                                           ⎟ (1)
                                                                                        ⎜                        255 2              ⎟
                                                                       CPSNR = 10 log10 ⎜        3   W    H                         ⎟
                                                                                                ∑∑∑ [I (i, j, k ) − I (i, j, k )]
                                                                                        ⎜                                           ⎟
                                                                                        ⎜ 3HW                    in      out        ⎟
                                                                                        ⎝       k =1 i =1 j =1                      ⎠
                                                                        2) PSNR comparison between mosaic images: It is hard to
                                                                     compare the CPSNR values in the proposed schemes outlined
                                                                     in section IV due to the involvement of the demosaicking and
                                                                     color balancing process in the path. Instead, PSNR is
                                                                     calculated between the original raw mosaic image Y and the
                                                                     reconstructed mosaic image Y’ in Fig. 3. The PSNR
                                                                     calculation is done by using equation (2). The corresponding
  Fig. 7. 5 Level Mallet packet wavelet decomposition of Isochart.
                                                                     compression ratio is calculated from the bitrate of coding Y’.

                                                                                          ⎛ 255 2 ⎞
                     V. EXPERIMENTAL SETUP                                                ⎜ d ⎟
                                                                          PSNR = 10 log10 ⎜       ⎟                                     (2)
                                                                                          ⎝       ⎠
  A. Test Images                                                        3) Visual comparison between the conventional and
  Test images used for our experiment are “raw” mosaic               proposed approaches: Due to the very different system setup,
images taken from Nikon D70 digital camera, which has a              CPSNR comparison between conventional and proposed
Bayer Pattern color filter array. A Matlab program ISET              approaches would not generate meaningful results. Visual
provided by Joyce Ferrell is used to extract data information        comparison is carried out between the final RGB pictures
of the raw mosaic images.                                            displayed to determine the difference in overall quality.
  B. Demosaicking Algorithm and Color Balancing
  A simple Laplacian demosaicking algorithm and ‘Gray
World’ color balancing algorithm supplied by the ISET tool                           VI. RESULTS AND ANAYLYSIS
was used to perform demosaicking and color balancing on all          The results presented in this section are based on the test
test images.                                                         image “People” and the setup outlined in the previous section.
                                                                     Fig. 10 (a) shows the “People” image in its uncompressed,
  C. R:G:B distortion ratio experiment                               demosaicked and color balanced form. This would correspond
   In Deinterleaved Lossy Compression, a natural way to              to the RGB image X in Fig. 2. This serves as a reference to the
performing bit allocation among the red, green and blue              best quality output a compression scheme can produce.
subimages is to distribute distortion evenly among the three
subimages so that each of them have the same average
   However, since the human visual system is more sensitive

  A. CPSNR Comparison of Conventional Approaches                                             image “people” compressed using the conventional approach
                                                                                             with RGB subchannels compressed independently. Due to the
                CPSNR vs Compression Ratio of Demosaicking-First Compression-Later Design    high compression ratio, the color picture quality is severely
                                                                   YCrCb compressed
                                                                                             deteriorated. Blocking artifacts caused by subband coding at
                36                                                 RGB compressed            low rates can be seen clearly.
                                                                                               On the other hand, Fig. 10 (c) shows the same image being
                                                                                             compressed with the proposed deinterleaved approach. With
                                                                                             very similar compression ratio, it has much better overall
   CPSNR (dB)

                33                                                                           quality and little artifacts. This comparison clearly shows that
                                                                                             the proposed deinterleaved approach outperforms the
                                                                                             conventional RGB compression.



                     2   4        6   8      10    12    14      16     18     20      22
                                            Compression Ratio

Fig. 8. CPSNR compression between the conventional approaches of test
image “People”

  The blue line representing compression done in the YCrCb
color space is higher then the red line representing
compression done in RGB space. This is expected behavior,
since color transform from RGB space to YCrCb space
decorrelates the interdependent red, green and blue channels,
thus resulting in a coding gain.

  B. PSNR Comparison between mosaic images
                              PSNR vs Compression Ratio of Raw Mosaic Image

                42                              Raw mosaic image compressed directly
                                                R, G, B compressed separately

                                                                                                              (b)                                    (c)
   PSNR (dB)





                  5          10       15      20        25         30         35        40
                                            Compression Ratio

Fig. 9. PSNR compression between the conventional approaches of test image                                    (d)                                    (e)
“People”                                                                                       Fig. 10. “People” results.
                                                                                               (a) Uncompressed, demosaicked and color balanced image
                                                                                               (b) Compressed using conventional approach, with RGB compressed
  The blue line, representing compression performed directly                                   separately. Compression ratio=14.39, CPSNR=29.33, distortion ratio of
on “raw” color mosaic image is higher then the red line,                                       R:G:B=1:1:1.
representing compression on separate RGB channels of “raw”                                     (c) Compressed using proposed deinterleaved approach. Compression
                                                                                               ratio=14.3, CPSNR=28.897, distortion ratio of R:G:B=1:1:1.
color mosaic image. The reason for this result is that as
                                                                                               (d) Compressed using conventional approach, with YCrCb compressed
discussed in section III, the 5/3 wavelet transform decorrelates                               separately. Compression ratio=15.09, CPSNR=30.62, distortion ratio of
the interdependent red, green and blue colors in the mosaic                                    Y:Cr:Cb=1:1:1.
image, thus giving rise to the coding gain observed.                                           (e) Compressed using proposed interleaved approach. Compression
                                                                                               ratio=14.45, CPSNR=30.074.

 C. Visual Comparison                                                                          2) Comparison of Conventional YCrCb Compression and
  1) Comparison of Conventional RGB Compression and                                          Proposed Interleaved Compression: Comparing Fig. 10 (d)
Proposed Deinterleaved Compression: Fig. 10 (b) shows the                                    and Fig. 10 (e) shows that the proposed interleaved approach

gives much better result then the YCrCb compressed                  similar visual quality. Superiority of images from one method
approach, especially in terms of color distribution. While Fig.     to the other largely depends on personal preference and the
10 (d) shows large blocks of underlying red and blue tone,          choice of image. However, since the interleaved approach
Fig. 10 (e) has rather natural color scheme and little noticeable   doesn’t require the separation of the mosaic image into red,
artifact.                                                           blue and green subimages, it has a simpler algorithm and often
  3) Comparison of Deinterleaved Compression and                    requires much less processing time. Thus, since the resulting
Interleaved Compression: By comparing Fig. 10 (c) and Fig.          compressed images are similar, the Interleaved approach,
10 (e), it is observed that under similar compression ratio, the    having an advantage in processing time, maybe a better choice
deinterleaved approach and the interleaved approach produce         overall.
color images of similar visual quality. It is hard to judge
which of the approaches is more superior to the other one.
Comparison of these two approaches using other test images
also results in the same conclusion that under the same               The following figures show the experimental results from
compression ratio, both approaches result in images of similar      additional test images that we have used for comparison.
visual quality. For the results of other images, please refer to
the Appendix.

                     VII.   FUTURE WORKS
During the progress of this work, we have identified several
interesting directions to extend this work. We will briefly
discuss them in this section.
1) In the proposed deinterleaved approach, wavelet
     transform is applied to each of the three color sub-
     channels. Although wavelet transform has a clear
     advantage for interleaved “raw” mosaic color image, it                                            (a)
     may not be the optimal choice for the de-interleaved
     image data since we are not exploiting its advantage of
     decorralating the three colors. Using other transform
     coders, such as DPCM, might give better results for the
     Deinterleaved approach.
2) While doing the experiment, it is noticed that the
     demosaic algorithm play a very important role in the final
     color image quality. Different demosaic algorithms can be
     explored to see what type of demosaic algorithms will be
     the most suitable one for our specific compression
                                                                                     (b)                                 (c)
3) In this paper, we have implemented the conventional
     compression pipelines such that the transform and
     compression schemes are the same as that of our
     proposed approaches. Further work can go into using well
     established standards, such as JPEG2000, to compress
     images in the conventional pipeline, and compare them to
     results of our proposed approaches.

                      VIII. CONCLUSION
   We have proposed two lossy compression schemes for                                (d)                                 (e)
“raw” color mosaic images based on the lossless compression           Fig. 16. “Isochart” results.
                                                                      (a) Uncompressed, demosaicked and color balanced image
schemes outlined in [1]. Our test results show that using a           (b) Compressed using conventional approach, with RGB compressed
compression-first,     demosaicking-later       design,   both        separately. Compression ratio=12.72, CPSNR=19.4, distortion ratio of
deinterleaved and interleaved compression methods                     R:G:B=1:1:1.
                                                                      (c) Compressed using proposed deinterleaved approach. Compression
outperform the conventional demosaicking-first compress-              ratio=12.9, CPSNR=19.28, distortion ratio of R:G:B=1:1:1.
later scheme. The visual quality of the final compressed color        (d) Compressed using conventional approach, with YCrCb compressed
images is significantly better then the ones produced using the       separately. Compression ratio=12.72, CPSNR=28.09, distortion ratio of
conventional approach.
                                                                       (e) Compressed using proposed interleaved approach. Compression
   Between the two proposed methods, deinterleaved and                ratio=13.02, CPSNR=27.93.
interleaved compression result in compressed color images of

                                                                                                     DIVISION OF WORK
                                                                            The amount of work is about equally shared among the two.
                                                                          The following is a rough breakdown.
                                                                            - Implement reference paths
                                                                            - Implement deinterleaved algorithm
                                                                            - Wavelet lifting
                                                                            - presentation
                                   (a)                                      - Implement interleaved algorithm
                                                                            - Mallet packet wavelet decomposition
                                                                            - SPIHT coding
                                                                            - report

                                                                          [1]   Ning Zhang and Xiaolin Wu. “Lossless Compression of Color Mosaic
                                                                                Images,” IEEE Trans. ImageProcessing, vol. 15, No. 6, pp. 1379–1388,
                                                                                June 2006.
                                                                          [2]   Y. Tim Tsai. “Color Image Compression for Single-Chip Cameras,”
                                                                                IEEE Trans. Electron Devices, vol. 38, No. 5, pp. 1226–1232, May
                 (b)                                 (c)                  [3]   Michael D. Adams, Faouzi Kossentini. “Reversible Integer-to-Integer
                                                                                Wavelet Transforms for Image Compression: Performance Evaluation
                                                                                and Analysis,” IEEE Trans. Image Processing, vol. 9, No. 6, pp. 1010–
                                                                                1024, June 2000.
                                                                          [4]   David Taubman, and Michael Marcellin, “JPEG2000 Image
                                                                                Compression Fundamentals, Standards, and Practice” Boston: Kluwer
                                                                                Academic Publishers, 2002.
                                                                          [5]   Xiang Xie, GuoLin Li, ZhiHua Wang, Chun Zhang, DongMei Li and
                                                                                XiaoWen Li. “A Novel Method of Lossy Image Compression for Digital
                                                                                Image Sensors with Bayer Color Filter Arrays,” in Conf. Rec. 2005 IEEE
                                                                                Int. Conf. Circuits and Systems, pp. 4995–4998.
                                                                          [6]   Chin Chye Koh, Jayanta Mukherjee, and Sanjit K. Mitra. “New Efficient
                                                                                Methods of Image Compression in Digital Cameras with Color Filter
                                                                                Array,” IEEE Trans. Consumer Electronics, vol. 49, No. 4, pp. 1448–
                                                                                1456, November 2003.
                 (d)                                 (e)

  Fig. 17. “women” results.
  (a) Uncompressed, demosaicked and color balanced image
  (b) Compressed using conventional approach, with RGB compressed
  separately. Compression ratio=11.67, CPSNR=29.38, distortion ratio of
  (c) Compressed using proposed deinterleaved approach. Compression
  ratio=11.44, CPSNR=29.34, distortion ratio of R:G:B=1:1:1.
  (d) Compressed using conventional approach, with YCrCb compressed
  separately. Compression ratio=11.42, CPSNR=34.35, distortion ratio of
  (e) Compressed using proposed interleaved approach. Compression
  ratio=11.36, CPSNR=32.03.

  We would like to thanks Markus Flierl, Joyce Farrell, and
Professor Brian Wandell for their great help on this project.