An improved Newton projection method for nonnegative deblurring of Poisson-corrupted images with Tikhonov regularization
- First Online:
- 187 Downloads
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.
KeywordsNonnegatively constrained minimization Regularization Image deblurring Newton projection method Poisson noise
Unable to display preview. Download preview PDF.
- 7.Bertsekas, D.: Nonlinear Programming, 2nd ed. Athena Scientific, Belmont, Massachusetts (1999)Google Scholar
- 17.Lanteri, H., Bertero, M., Zanni, L.: Iterative image reconstruction: a point of view. In: Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT) (CRM Series, vol. 7), pp. 37–63 (2008)Google Scholar