Linear pre/post filters for transform and subband/wavelet coding

We propose a novel method for designing linear pre/post filters for transform and subband/wavelet coders. We use a linear gain-plus-additive noise model to describe the effects of a class of point distribution function-optimized quantizers. Using this quantizer model, we provide an explicit expression for the power spectral density of the reconstruction error in an improved transform coding system that includes linear pre/post filters. This expression allows us to design pre/post filters that minimize the overall mean square error at a given target rate, by improving the frequency domain behavior of the overall system. For a 1-D Gauss-Markov source, we show that pre/post filters help DCT-based coders to match the performance of subband coders. We also describe an a posteriori method of designing postfilters for a JPEG coder, that uses the actual image data and maximizes the PSNR performance of the system. The postfilter coefficients are designed at the transmitter, and are sent to the receiver as part of the coded data.