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 the subband signal is combined with the statistical model of the input signal to derive the multirate state-space model for a filter bank system with additive noise. Thus the signal reconstruction problem in the 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 the 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.