# - Acharya T.

ISBN 0-471-48422-9

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F'(u,v) = Fq(u,v) x Q{u,v),

where Q(u,v) is the quantization step-size parameter from the same quantization table that was used during the compression process. After dequantization, the DCT coefficients F'(u,v) are inverse transformed to spatial domain data via inverse DCT (IDCT). IDCT of the 8x8 block F'(u,v) for (u, v = 0,1, â€˘ â€˘ â– , 7) is defined by:

1 7 7

f(x, V) = 0(u)C(v)F'{u, v) cos

u=0 i/=0

for x = 0,1,..., 7 and y = 0,1,..., 7.

After decompression of all the MCUs from the compressed bitstream, the image components are reconstructed and stored. For grayscale image, there is only one component and no color transformation is required. For color image, the reconstructed Y, Cb, and Cr components are inverse transformed to RGB color space. We show a picture of the famous â€śPeppersâ€ť image in Figure 3.6(a). The color version of Figure 3.6 is provided in the color figures page. The image is compressed using the baseline JPEG algorithm with quality factor Q-JPEG = 75 and the reconstructed image is perceptually almost identical to the original image. This is shown in Figure 3.6(b). When we compress the same image with quality factor Q-JPEG = 10, we can see prominent artifacts in the image as shown in Figure 3.6(c). The nature of artifacts that is caused by lossy JPEG compression/decompression is called blocking artifacts. This happens because of the discontinuities created at the 8x8 block boundaries, since the blocks are compressed and decompressed independently. The new JPEG2000 standard solves this problem by using Discrete Wavelet Transform over the whole image. Figure 3.6(d) shows the result of the JPEG2000 standard compressing the image with the same bitrate (0.24 bits per pixel). The details of this new standard will be discussed in Chapter 6.

n(2x + l)u

16

cos

7r(2 y + l)t)

16

74 JPEG: STILL IMAGE COMPRESSION STANDARD

Fig. 3.6 (a) Original Pepper image, (b) compressed with baseline JPEG using quality factor 75 (1.57 bit/pixel), (c) compressed with baseline JPEG using quality factor 10 (0.24 bit/pixel), and (d) compressed with the new JPEG2000 standard using the same bit rate (0.24 bit/pixel).

PROGRESSIVE OCT-BASED MODE

75

3.4 PROGRESSIVE DCT-BASED MODE

One of the major disadvantages of the single scan sequential DCT-based mode (baseline JPEG) of compression is that the entire image cannot be rendered or viewed until the whole compressed bitstream is received and decoded. This is not desirable for many applications such as image browsing applications. In image browsing applications, the user is not expected to wait until the whole bitstream is decoded before viewing the entire image. It is desirable to the user that one can browse an initial appearance of the image and then choose to continue for finer detail or stop. This is possible in progressive DCT-based mode in JPEG.

In progressive DCT-based mode, the image is coded sequentially in multiple scans. Idea of this mode is to transmit a coarser version of the image in the first scan and then progressively improve the reconstructed quality at the receiver by transmitting more compressed bits in successive scans. In progressive coding mode, the DCT blocks of the entire image are computed first before entropy encoding of a block can start. Hence implementation of this mode requires the availability of a buffer that can contain all the DCT coefficients of the whole image. The entropy encoding method then selectively encodes the DCT coefficients and transmits. There are two complementary ways to achieve this partial encoding of the DCT blocksâ€”spectral selection and successive approximation. Examples of these two methods have been shown in Figure 3.7.

In the spectral selection mode of progressive coding, all the DCT coefficients in an 8 x 8 data block are not encoded in one scan. Instead it encodes sets of DCT coefficients starting from lower frequencies and moving progressively to higher frequencies. For example, we can encode all the DC coefficients of all the 8x8 DCT blocks in the first scan as shown in Figure 3.7(a). In the second scan we can encode and transmit the first three AC coefficients of the zig-zag sequence of all the DCT blocks. We can transmit the next three AC coefficients in the third scan, and so on. The last three AC coefficients can be transmitted in the 21st scan as shown in Figure 3.7(a). The number of coefficients in each scan could be different and user selectable. This progressive coding scheme is simple to implement. The result of this method is that reconstructed images at the earlier scans are blurred and the image gets sharper in the successive scans.

In successive approximation mode of progressive coding, a certain number of most significant bits (say N\) of all the DCT coefficients of all the blocks are encoded and transmitted in the first scan. In the second scan, the following N2 most significant bits are encoded and transmitted and so on. We show this method in Figure 3.7(b) as an example. In this figure, the most significant three bits of all the DCT coefficients are encoded and transmitted in the first scan. Then we can choose to encode and transmit the next 1 bit of all the DCT coefficients in each of the successive scans and continue until the least significant bit of all the coefficients is encoded. Usually the successive approx-

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