Numerical Algorithms

, Volume 60, Issue 1, pp 169–188

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


    • Department of MathematicsUniversity of Bologna
  • Elena Loli Piccolomini
    • Department of MathematicsUniversity of Bologna
Original Paper

DOI: 10.1007/s11075-011-9517-y

Cite this article as:
Landi, G. & Loli Piccolomini, E. Numer Algor (2012) 60: 169. doi:10.1007/s11075-011-9517-y


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.


Nonnegatively constrained minimizationRegularizationImage deblurringNewton projection methodPoisson noise
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© Springer Science+Business Media, LLC. 2011