Projections Onto Convex Sets through Particle Swarm Optimization and its application for remote sensing image restoration

Image restoration attempts to enhance images corrupted by noise and blurring effects. Iterative approaches can better control the restoration algorithm in order to find a compromise of restoring high details in smoothed regions without increasing the noise. Techniques based on Projections Onto Convex Sets (POCS) have been extensively used in the context of image restoration by projecting the solution onto hyperspaces until some convergence criteria be reached. It is expected that an enhanced image can be obtained at the final of an unknown number of projections. The number of convex sets and its combinations allow designing several image restoration algorithms based on POCS. Here, we address two convex sets: Row-Action Projections (RAP) and Limited Amplitude (LA). Although RAP and LA have already been used in image restoration domain, the former has a relaxation parameter (λ) that strongly depends on the characteristics of the image that will be restored, i.e., wrong values of λ can lead to poorly restoration results. In this paper, we proposed a hybrid Particle Swarm Optimization (PSO)-POCS image restoration algorithm, in which the λ value is obtained by PSO to be further used to restore images by POCS approach. Results showed that the proposed PSO-based restoration algorithm outperformed the widely used Wiener and Richardson–Lucy image restoration algorithms.