An image reconstruction method from Fourier data with uncertainties on the spatial frequencies

3rd International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Cornelio, Anastasia^1 ; Bonettini, Silvia^2 ; Prato, Marco^1

Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via Campi 213/b, 41125 Modena, Italy^1

Dipartimento di Matematica e Informatica, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy^2

关键词: Alternating minimization;    Astronomical application;    Constrained minimization;    Gradient projection methods;    Image reconstruction methods;    Nonuniform sampling;    Optimization problems;    Two dimensional images;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/464/1/012008/pdf
DOI  :  10.1088/1742-6596/464/1/012008

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

In this paper the reconstruction of a two-dimensional image from a nonuniform sampling of its Fourier transform is considered, in the presence of uncertainties on the frequencies corresponding to the measured data. The problem therefore becomes a blind deconvolution, in which the unknowns are both the image to be reconstructed and the exact frequencies. The availability of information on the image and the frequencies allows to reformulate the problem as a constrained minimization of the least squares functional. A regularized solution of this optimization problem is achieved by early stopping an alternating minimization scheme. In particular, a gradient projection method is employed at each step to compute an inexact solution of the minimization subproblems. The resulting algorithm is applied on some numerical examples arising in a real-world astronomical application.