Subband coding is a popular and well established technique used in multimedia communications, such as audio, image and video transmission. In the absence of quantization and transmission errors, the analysis and synthesis filters in a subband coding scheme can be designed to obtain perfect reconstruction of the input signal, but this is no longer the optimal solution in the presence of quantization of the subband coefficients. In this paper, we analyze the problem of optimal design of the synthesis filters in a subband coding system. To simplify the filter design, we model the input signal as a first-order Markov process, whose correlation parameters can be easily estimated from the input data. The use of a statistical model for the input signal makes the design technique efficient and the problem of an M-subband filter bank design tractable. The approach is extended to image coding using a sub-optimal separable solution, in which the input image is modeled as a 2D separable Markov process plus additive white noise. The extension to the 2D case is not trivial, since the processing in one direction, e.g., the rows, alters the statistics of the signals for the design of the filters in the other direction, e.g., the columns. We show that the filters designed using the model can give a significant gain with respect to the perfect reconstruction solution, especially when the dither technique is used for quantization. Design examples for 1D signals and images are shown.
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