A Novel Gradient Projection Approach for Fourier-Based Image Restoration

Journal Article · Thu Sep 30 00:00:00 EDT 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3498529· OSTI ID:21428609

Bonettini, S ^[1]; Prato, M ^[2]

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1. Dipartimento di Matematica, Universita di Ferrara, Via Saragat 1, 44122 Ferrara (Italy)
2. Dipartimento di Matematica, Universita di Modena e Reggio Emilia, Via Campi 213/b, 41125 Modena (Italy)

This work deals with the ill-posed inverse problem of reconstructing a two-dimensional image of an unknown object starting from sparse and nonuniform measurements of its Fourier Transform. In particular, if we consider a priori information about the target image (e.g., the nonnegativity of the pixels), this inverse problem can be reformulated as a constrained optimization problem, in which the stationary points of the objective function can be viewed as the solutions of a deconvolution problem with a suitable kernel. We propose a fast and effective gradient-projection iterative algorithm to provide regularized solutions of such a deconvolution problem by early stopping the iterations. Preliminary results on a real-world application in astronomy are presented.

• OSTI ID: 21428609
• Journal Information: AIP Conference Proceedings, Vol. 1281, Issue 1; Conference: ICNAAM 2010: International conference of numerical analysis and applied mathematics 2010, Rhodes (Greece), 19-25 Sep 2009; Other Information: DOI: 10.1063/1.3498529; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
ALGORITHMS
ASTRONOMY
FOURIER TRANSFORMATION
IMAGE PROCESSING
IMAGES
ITERATIVE METHODS
MATHEMATICAL SOLUTIONS
OPTIMIZATION
TWO-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
INTEGRAL TRANSFORMATIONS
MATHEMATICAL LOGIC
PROCESSING
TRANSFORMATIONS