Constrained least-squares filtering for noisy images blurred by random point spread function

Abstract

A restoration filter based on the constrained least-squares principle is proposed for the restoration of images distorted by random point spread function and additive measurement noise. The proposed filter modifies the conventional constrained least-squares filter by incorporating the second-order statistics, such as correlations, about the randomness of the point spread function. For space-invariant imaging systems, the proposed filter can be implemented in the discrete frequency domain and its computations can be carried out using the fast Fourier transform. Simulation results show that the proposed filter outperforms the conventional constrained least-squares filter, which neglects the correlations of the random point spread function.