A comparison of reconstructed image quality is made between block-pruned sizes of 1 × 1, 2 × 2 and 3 × 3 with that of 1,4 and 9 zigzag pruned coefficients respectively. Table 2.8 Shows the PSNR comparison between block pruned DTT and zigzag pruned DTT. It can be observed that the PSNR of reconstructed images using 9 zigzag pruned coefficients are higher than that of 3 × 3 block-pruned image sizes. Comparing with 4 zigzag pruned coefficients and 2 × 2 block pruned coefficients, the PSNR of block pruned coefficients are higher. Nevertheless, there is advantage of computational complexities in both cases. Similarly, comparison is made between block-pruned DTT with block-pruned DCT and zigzag-pruned DTT with zigzag-pruned DCT in Table 2.9. It has seen observed that 9 zigzag pruned coefficients of DTT/DCT show always a higher PSNR than that of 3 × 3 block-pruned coefficients. For example, in case of Lena image, 9 zigzag pruned DTT shows a PSNR gain of 0.7 dB, Barbara shows a significant gain of 1.54 dB and Crowd image shows a PSNR gain of 1.02 dB. Similar performance improvement is also noticed in 9 zigzag pruned DCT images shown in
Table 2.10 and 2.11. Furthermore, for images such as Lena, Barbara and Crowd of Table 2.10, DCT shows slight better performance than that of DTT. For images such as Finger print, Mountain and Library of Table 2.11, DTT outperforms DCT of any pruning sizes. For instance, Finger print image shows a PSNR gain of 1.27 dB in 9- prune sizes and 0.27 dB in 4-prune sizes. For Mountain and Library images the PSNR gain is slightly higher. Hence, 9 zigzag pruned coefficients are enough for practical image or video coding applications.
Table 2.8: Comparison of PSNR between block-pruned and zigzag-pruned reconstructed images of (a) Lena, (b) Barbara and (c) Crowd.
No. of DTT PSNR(dB)
coefficients Lena Barbara Crowd
retained Block prune Zigzag prune Block prune Zigzag prune Block prune Zigzag prune
1 26.92 26.92 23.37 23.37 21.62 21.62
4 33.35 32.35 25.61 25.23 30.13 29.43
9 39.29 40.00 30.03 31.57 38.54 39.59
Table 2.9: Comparison of PSNR between block-pruned and zigzag-pruned reconstructed images of (d) Finger print, (e) Mountain, and (f) Library.
No. of DTT PSNR(dB)
coefficients Finger print Mountain Library
retained Block prune Zigzag prune Block prune Zigzag prune Block prune Zigzag prune
1 11.08 11.08 17.08 17.08 16.25 16.25
4 14.94 16.84 19.60 19.82 18.90 19.44
9 22.28 24.38 22.97 23.17 22.69 23.45
Table 2.10: Comparison of PSNR between DCT and DTT of block pruned and zigzag pruned reconstructed images of (a) Lena, (b) Barbara and (c) Crowd.
No. of PSNR(dB)
coefficients Lena Barbara Crowd
retained for Block prune Zigzag prune Block prune Zigzag prune Block prune Zigzag prune image DCT DTT DCT DTT DCT DTT DCT DTT DCT DTT DCT DTT reconstruction 1 26.92 26.92 26.92 26.92 23.37 23.37 23.37 23.37 21.62 21.62 21.62 21.62 4 33.43 33.36 32.38 32.35 25.68 25.61 25.29 25.23 30.20 30.12 29.47 29.43 9 39.65 39.29 40.24 39.99 30.29 30.03 31.78 31.57 39.15 38.54 40.03 39.59
2.7
Conclusions
In this chapter, an 8 × 8 DTT algorithm is implemented in the JPEG in place of 8 × 8 DCT algorithm. By using various test images, it has been observed that DTT has energy compaction property competitive with that of DCT and thereby provides compression performance relatively close with DCT. Therefore, it can be a suitable
Table 2.11: Comparison of PSNR between block-pruned and zigzag-pruned reconstructed images of (d) Finger print, (e) Mountain, and (f) Library.
No. of PSNR(dB)
coefficients Finger print Mountain Library
retained for Block prune Zigzag prune Block prune Zigzag prune Block prune Zigzag prune image DCT DTT DCT DTT DCT DTT DCT DTT DCT DTT DCT DTT reconstruction
1 21.88 21.88 21.88 21.88 17.07 17.07 17.07 17.07 16.25 16.25 16.25 16.25 4 28.05 28.25 29.11 29.38 19.59 19.59 19.80 19.82 18.90 18.90 19.42 19.44 9 30.42 30.75 31.94 33.21 22.96 22.97 23.16 23.17 22.69 22.69 23.42 23.45
candidate for applications such as PDA, mobile phones and digital cameras where ef- ficient image compression techniques are required. The proposed technique uses same quantization matrix and zigzag scan pattern as used in JPEG standard. The perfor- mance of DTT can be improved further by suitably selecting a proper quantization matrix and adaptive scanning technique.
A novel hybrid HVS based DTT SPIHT embedded image coding algorithm has been proposed. It has been demonstrated that the proposed image coding algorithm shows an impressive PSNR gain over standard baseline JPEG, EZDCT and STQ, at all bit-rates but comparable with Improved JPEG, STQ+Haar and DCT SPIHT on smooth and textured images. DTT SPIHT consistently outperforms DCT SPIHT for images having sharp edges. By incorporating HVS, the perceptual quality of the proposed algorithm has been improved at a little cost of PSNR values. This is especially noticeable at bit-rates ≤ 0.5 bpp. Future research direction is to use adaptive HVS and modified SPIHT algorithm, which is expected to improve the image quality subjectively and objectively at low bit-rates.
Finally, a fast algorithm of 2-D 4 × 4 DTT has been proposed which pruned the coefficients in a zigzag fashion. This zigzag order pruning can be more suitable for still images and video coding applications because of considerable improvement in objective image quality and fast processing. The pruning algorithm is implemented in a Xilinx XC2VP30 FPGA, which shows considerable amount of hardware savings than a 4 × 4 floating point DTT. Furthermore, it has been shown that compression using DTT is very similar to compression using DCT for natural and artificial images. Further research work in this field can be extended to develop a fast DTT algorithm for input block of size 8 × 8.
Low Complexity Embedded Image
Compression Algorithm Using
Hierarchical Listless DTT
Preview
Listless set partitioning embedded block (LSK) and Set partitioning embedded block (SPECK) are known for their low complexity and simple implementations. However, the drawback is that these block based algorithms encode each insignificant subband by a zero. Therefore, these algorithms generate many zeros at earlier passes. It is known from the statistics of transformed images that the numbers of significant co- efficients at higher bitplanes are likely to be very few. An improved LSK (ILSK) algorithm that codes a single zero to several insignificant subbands has proposed. This reduces the length of the output bit string, encoding/decoding time and mem- ory requirement at early passes. Further, ILSK algorithm has been coupled with discrete Tchebichef transform (DTT). The proposed new coder named as Hierarchi- cal listless DTT (HLDTT) has some desirable attributes like full embeddedness for progressive transmission, precise rate control for constant bit-rate traffic, region of in- terest retrievability and low complexity for low power applications. The performance of HLDTT is assessed using PSNR and MSSIM. From the simulation result, HLDTT shows significant improvement in PSNR values from lower to medium bit rates. At the same time, HLDTT shows an improvement in MSSIM values over most of the DCT based embedded coders on all bit rates.
3.1
Introduction
Hand held mobile or portable devices have limited memory, processing power and battery life. Real time processing and transmission of images using these devices
require an image coding algorithm that can compress efficiently with reduced com- plexity. Wavelet based image coders such as Embedded zerotree wavelet coder (EZW) [15], Set partitioning in hierarchical trees (SPIHT) [16], Set partitioning embedded block (SPECK) [26], Morphological representations of wavelet data (MRWD)[79] and Significance-linked connected component analysis (SLCCA) [80] provide excellent rate distortion performances by exploiting magnitude correlation within or across bands of decomposition. Each of these coders generates a fidelity progressive bit stream by encoding bit-planes of quantized dyadic subband coefficients.
SPIHT exhibits much better performance over EZW due to additional partitioning steps. The SPIHT algorithm has low complexity. However, being a tree based algo- rithm, it is memory intensive. SPECK is a block based distortion scalable embedded coder. It uses recursive block splitting methods to isolate significant coefficients. It has excellent coding performance with very low computational complexity. However, it requires memory intensive operation as it uses list structure. A variant of SPIHT called NLS which uses a state table with four bits per coefficient to keep track of set partitions is presented in [35]. Latte et al. [36] presented a listless SPECK (LSK) algorithm which uses special markers as in NLS. These markers are updated as block splitting forms new significant blocks.
Though SPECK and LSK are low complexity image coding algorithms with perfor- mance nearly close to SPIHT, these coders do not fully exploit the coding performance at lower bit rates. By looking at the statistics of transformed images, the number of significant coefficients whose magnitudes are higher than certain thresholds are very few on earlier bitplane passes. Since LSK does an explicit breadth first search, it codes zeros to each insignificant subbands as it moves from coarsest to finest sub- bands. There could be six to seven bit plane passes where LSK codes many zeros as many subbands are likely to be insignificant with respect to early thresholds. A block-tree based wavelet algorithm presented in [33] exploits both inter and intra sub- band correlations to improve the coding performance at very low bit rates. However, it uses depth first scanning and processes ordered list arrays for set partitioning.
In this chapter, an improved LSK algorithm (ILSK) which combines with DTT has been proposed. The proposed new coder which combines DTT with ILSK is named as Hierarchical Listless DTT (HLDTT) is proposed. HLDTT not only re- duces the encoder and decoder complexity, but also improves the coding efficiency at lower bit rates. This is achieved by comparing magnitude of coefficients within and across several subbands/levels. A combination of DTT with LSK coder (named as DTT LSK) is also proposed to test the effectiveness of HLDTT. The performance of these coders are evaluated and compared with some of DCT based embedded coders.
It has been found that the proposed coders DTT LSK and HLDTT outperforms al- most all DCT based embedded coders at lower bit rates. The performance of HLDTT with Integer wavelet transformed based SPIHT (IWT SPIHT) [89], discrete wavelet transformed/Lift based SPIHT [10] (DWT SPIHT)[90],[91] and JPEG 2000 [92] is also compared. It is observed that HLDTT shows an average of 1.0 dB PSNR reduc- tion over the JPEG 2000 on considered bit rates. The performance of all these coders are also assessed using state-of-the-art image quality metric MSSIM [3]. It is found that the proposed coder outperforms DCT SPIHT on all the bit rates for most of the images.