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A Nonadaptive Optimal Transform Coding System
ChengHsiung HSIEH
Publication
IEICE TRANSACTIONS on Communications
Vol.E86B
No.11
pp.32663277 Publication Date: 2003/11/01 Online ISSN:
DOI: Print ISSN: 09168516 Type of Manuscript: PAPER Category: Multimedia Systems Keyword: optimality, transform coding, image compression, coefficient selection, JPEG,
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Summary:
In this paper, a nonadaptive optimal transform (NAOT) coding system is proposed. Note that the energyinvariant property in an orthogonal transformation and that the mean squared error (MSE) of a reconstructed image is proportional to the total energy of transform coefficients discarded in the coding process. The NAOT coding system is developed and proved optimal in the sense of minimum average energy loss. Basically, the proposed coding system consists of the following steps. First, obtain the average energy image block from transform image blocks. Second, sort the average energy image block in the descending order by energy where the sorted indices are recorded. Third, specify the number of coefficients, M, to be retained in the coding process. Fourth, the first M sorted indices form a set denoted as S_{M} through which the problem of optimal feature selection in transform coding is solved. Fifth, find a fixed mask A_{M} from set S_{M} which is then used to select M significant transform coefficients in image blocks. Finally, the M selected coefficients are quantized and coded by the order as in S_{M}. To verify the NAOT coding system, simulations are performed on several examples. In the simulation, the optimality and the optimal feature selection in the NAOT coding system are justified. Also, the effectiveness of the proposed S_{M}based selection approach is compared with the zigzag scan used in the JPEG. For fair comparison, the JPEG is modified to code only M transform coefficients. Simulation results indicate that the performance of S_{M}based selection approach is superior or identical to the zigzag scan in terms of PSNR. Finally, the performance comparison between the NAOT coding system and the JPEG is made. It suggests that the proposed NAOT coding system is able to trade very little PSNR for significant bit rate reduction when compared with the JPEG. Or it can be said that the JPEG wastes much bit rate to improve very little PSNR on the reconstructed image, when compared with the NAOT coding system.

