State space approach to constrained recursive deconvolution of a noisy image sequence

It is well known that constrained recursion techniques can be used to restore images degraded by convolutional filters. The recursion which is commonly used was designed to work on a single noise-free image frame and convergence conditions were derived via the contraction mapping theorem. However these conditions do not guarantee convergence when the degrading filter has zeros in its transfer function. The authors consider the case where the imaging system gathers a sequence of noisy images of a static scene. The problem formulation uses a state space approach to provide easily verifiable conditions on the degrading filter which guarantee that the scene can be recovered from the image sequence in the presence of noise. It is shown that even transfer functions which have zeros are allowed. A recursive filter is developed to construct the estimate of the scene from the image sequence and experimental results are given