An Optimal Transform Image Coding

Abstract

In this paper, an optimal transform image coding (OTIC) system is proposed. Note that the energy-invariant property in orthogonal transformation and that the mean squared error (MSE) of reconstructed image is proportional to the total energy of transform coefficients discarded in the coding process. The OTIC system is developed and is proved optimal in the sense of minimum average energy loss. Basically, the proposed coding system consists of three phases. First, the average energy image block is obtained from transform image blocks. Next, indices of average energy image block are sorted in descending order by energy. When the number of coefficients to be retained, M, in the coding process is determined, the first M elements in reordered indices form a set denoted as M S . Then a fixed mask M A acquired from set M S is used to select M significant coefficients in transform image blocks. Finally, the M selected coefficients are quantized and coded by the order as in M S . Simulations are provided to justify the optimality in the proposed OTIC system. Besides, the effectiveness of the proposed selection approach, which is based on M S , is compared with the zigzag scan used in JPEG. Simulation results indicate that the M S -based selection approach is superior, in terms of PSNR, to the zigzag scan in most of cases.