Multiple-image deblurring with spatially-variant point spread functions

¹ Chip Computers Consulting s.r.l., Viale Don L. Sturzo 82, S.Liberale di Marcon, 30020 Venice, Italy e-mail: robertovio@tin.it
² ESA-VILSPA, Apartado 50727, 28080 Madrid, Spain
³ Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA e-mail: nagy@mathcs.emory.edu
⁴ ESA-VILSPA, Apartado 50727, 28080 Madrid, Spain e-mail: willem.wamsteker@esa.int

Received: 27 November 2003
Accepted: 3 January 2005

Abstract

We generalize a reliable and efficient algorithm, to deal with the case of spatially-variant PSFs. The algorithm was developed in the context of a least-square (LS) approach, to estimate the image corresponding to a given object when a set of observed images are available with different and spatially-invariant PSFs. Noise is assumed additive and Gaussian. The proposed algorithm allows the use of the classical LS single-image deblurring techniques for the simultaneous deblurring of the observed images, with obvious advantages both for computational cost and ease of implementation. Its performance and limitations, also in the case of Poissonian noise, are analyzed through numerical simulations. In an appendix we also present a novel, computationally efficient deblurring algorithm that is based on a Singular Value Decomposition (SVD) approximation of the variant PSF, and which is usable with any standard space-invariant direct deblurring algorithm. The corresponding Matlab code is made available.