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A quasi-Newton projection method for nonnegatively constrained image deblurring

elena loli piccolomini(piccolom***at***dm.unibo.it)
germana landi(landig***at***dm.unibo.it)

Abstract: In this paper we present a quasi-Newton projection method for image deblurring. The mathematical problem is a constrained minimization problem, where the objective function is a regularization function and the constraint is the positivity of the solution. The regularization function is a sum of the Kullback-Leibler divergence, used to minimize the error in the presence of Poisson noise, and of a Tikhonov term. The Hessian of the regularization function is approximated in order to invert it using Fast Fourier Transforms. The numerical experiments on some astronomical images blurred by simulated Point Spread Functions show that the method gives very good results both in terms of relative error and computational efficiency.

Keywords: Nonnegatively constrained minimization, regularization, image de- blurring, projected-Newton method, Poisson noise.

Category 1: Applications -- Science and Engineering (Basic Sciences Applications )

Category 2: Nonlinear Optimization (Bound-constrained Optimization )


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Entry Submitted: 11/21/2010
Entry Accepted: 11/21/2010
Entry Last Modified: 11/21/2010

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