Optimum pre- and postfilters for quantization

We consider the optimization of pre- and post filters surrounding a uniform quantizer such that the mean square error due to quantization is minimized. Unlike some previous work, the postfilter is not restricted to be the inverse of the prefilter. With no order constraint on the filters, we present closed form solutions for the optimum pre- and post filters. Using these optimum solutions, we obtain a coding gain expression for the system under study. We then repeat the same analysis with first order pre- and post filters in the form 1+αz^-1 and 1/(1+γz^-1) providing some examples where we compare coding gain performance with the case of α=γ

Multirate Kalman filtering approach for optimal two-dimensional signal reconstruction from noisy subband systems

The International Conference on Image Processing, Santa Barbara, California, 26-29 October 1997Conventional synthesis filters in subband systems lose their optimality when additive noise due, for example, to signal quantization, disturbs the subband components. The multichannel representation of subband signal is combined with the statistical model of input signal to derive the multirate state-space model for filter bank system with additive noises. Thus the signal reconstruction problem in subband system can be formulated as the process of optimal state estimation in the equivalent multirate state-space model. With the input signal embedded in the state vector, the multirate Kalman filtering provides the minimum-variance reconstruction of input signal. Using the powerful Kronecker product notation, the results and derivations can then be extended to the 2-D cases. Incorporated with the vector dynamical model, the 2-D multirate state-space model for 2-D Kalman filtering is developed. Computer simulation with the proposed 2-D multirate Kalman filter gives favorable results.published_or_final_versio

Model-based multirate Kalman filtering approach for optimal two-dimensional signal reconstruction from noisy subband systems

Conventional synthesis filters in subband systems lose their optimality when additive noise (due, for example, to signal quantization) disturbs the subband components. The multichannel representation of subband signals is combined with the statistical model of input signal to derive the multirate state-space model for the filter bank system with additive subband noises. Thus the signal reconstruction problem in subband systems can be formulated as the process of optimal state estimation in the equivalent multirate state-space model. Incorporated with the vector dynamical model, a 2-D multirate state-space model suitable for 2-D Kalman filtering is developed. The performance of the proposed 2-D multirate Kalman filter can be further improved through adaptive segmentation of the object plane. The object plane is partitioned into disjoint regions based on their spatial activity, and different vector dynamical models are used to characterize the nonstationary object-plane distributions. Finally, computer simulations with the proposed 2-D multirate Kalman filter give favorable results. ©1998 Society of Photo-Optical instrumentation Engineers.published_or_final_versio