Constrained signal restoration via iterated extended Kalman filtering

The problem of estimating the input (signal restoration) to a known linear system (point spread function), given the noisy observations of the output, is considered. The input signal is assumed to satisfy certain known physical constraints such as positivity. It is proposed to incorporate the constraints by introducing a memoryless non-linearity in the system. A statistical approach is taken leading to a closed-form type of recursive solution in the form of iterated extended Kalman filtering with two local iterations at every new data point. A simulation example is presented which demonstrates the superiority of the proposed approach over the conventional Kalman/Wiener filtering.