An improved Newton projection method for nonnegative deblurring of Poisson-corrupted images with Tikhonov regularization

Authors:
Germana Landi;Elena Loli Piccolomini
Affiliations:
Department of Mathematics, University of Bologna, Bologna, Italy;Department of Mathematics, University of Bologna, Bologna, Italy
Venue:
Numerical Algorithms
Year:
2012

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Abstract

In this paper a quasi-Newton projection method for image deblurring is presented. The image restoration problem is mathematically formulated as a nonnegatively constrained minimization problem where the objective function is the sum of the Kullback---Leibler divergence, used to express fidelity to the data in the presence of Poisson noise, and of a Tikhonov regularization term. The Hessian of the objective function is approximated so that the Newton system can be efficiently solved by using Fast Fourier Transforms. The numerical results show the potential of the proposed method both in terms of relative error reduction and computational efficiency.