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 dynamic model, a 2D multirate state-space model suitable for 2D Kalman filtering is developed. The performance of the proposed 2D 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 2D multirate Kalman filter give favorable results.