Linear pre/post filters for DCT-based image coding systems

We propose a novel method for designing linear, space-invariant pre/post filters for DCT-based image coders that minimize the mean square error. We use a linear gain-plus-additive noise model to describe the effects of a class of entropy-coded uniform threshold quantizers. Using this quantizer model and a homogeneous random field model for the input source, we derive an explicit expression for the power spectral density of the reconstruction error in an improved transform coding system that includes pre/post filters. Linear pre/post filters are subsequently designed that minimize the overall mean square error for a given input source and target rate. The postfilter coefficients are designed at the transmitter, and are sent to the receiver as part of the coded data. Such pre/post filters improve the frequency domain behavior of the system, when coding random fields. However, when coding natural images, one must account for spatial errors as well, such as blocking artifacts. We therefore develop an a posteriori method of designing linear postfilters that uses the actual image data and maximizes the PSNR performance of the system. We present simulation results that show that pre/post filters can help DCT-based coders to match the performance of subband/wavelet coders. We design short, adaptive, linear postfilters for the Baseline JPEG coder that surpass the PSNR performance of other post-processing methods described in the literature. © 1998 SPIE and IS&T.