A Non-adaptive Optimal Transform Coding System

Cheng-Hsiung HSIEH

A Non-adaptive Optimal Transform Coding System

Cheng-Hsiung HSIEH

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In this paper, a non-adaptive optimal transform (NAOT) coding system is proposed. Note that the energy-invariant 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.

Publication: IEICE TRANSACTIONS on Communications Vol.E86-B No.11 pp.3266-3277

Publication Date: 2003/11/01

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Type of Manuscript: PAPER

Category: Multimedia Systems

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Cheng-Hsiung HSIEH, "A Non-adaptive Optimal Transform Coding System" in IEICE TRANSACTIONS on Communications, vol. E86-B, no. 11, pp. 3266-3277, November 2003, doi: .
Abstract: In this paper, a non-adaptive optimal transform (NAOT) coding system is proposed. Note that the energy-invariant 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.
URL: https://global.ieice.org/en_transactions/communications/10.1587/e86-b_11_3266/_p

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@ARTICLE{e86-b_11_3266,
author={Cheng-Hsiung HSIEH, },
journal={IEICE TRANSACTIONS on Communications},
title={A Non-adaptive Optimal Transform Coding System},
year={2003},
volume={E86-B},
number={11},
pages={3266-3277},
abstract={In this paper, a non-adaptive optimal transform (NAOT) coding system is proposed. Note that the energy-invariant 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.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - A Non-adaptive Optimal Transform Coding System
T2 - IEICE TRANSACTIONS on Communications
SP - 3266
EP - 3277
AU - Cheng-Hsiung HSIEH
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Communications
SN -
VL - E86-B
IS - 11
JA - IEICE TRANSACTIONS on Communications
Y1 - November 2003
AB - In this paper, a non-adaptive optimal transform (NAOT) coding system is proposed. Note that the energy-invariant 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.
ER -