Quasi-Newton projection methods and the discrepancy principle in image restoration

Quasi-Newton projection methods and the discrepancy principle in image restoration

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Article ID: iaor20118981
Volume: 218
Issue: 5
Start Page Number: 2091
End Page Number: 2107
Publication Date: Nov 2011
Journal: Applied Mathematics and Computation
Authors: ,
Keywords: heuristics
Abstract:

In this work, the problem of the restoration of images corrupted by space invariant blur and noise is considered. This problem is ill‐posed and regularization is required. The image restoration problem is formulated as a nonnegatively constrained minimization problem whose objective function depends on the statistical properties of the noise corrupting the observed image. The cases of Gaussian and Poisson noise are both considered. A Newton‐like projection method with early stopping of the iterates is proposed as an iterative regularization method in order to determine a nonnegative approximation to the original image. A suitable approximation of the Hessian of the objective function is proposed for a fast solution of the Newton system. The results of the numerical experiments show the effectiveness of the method in computing a good solution in few iterations, when compared with some methods recently proposed as best performing.

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