A simple but efficient algorithm for multiple-image deblurring

¹ Chip Computers Consulting srl, Viale Don L. Sturzo 82, S.Liberale di Marcon, 30020 Venice, Italy
² ESA-VILSPA, Apartado 50727, 28080 Madrid, Spain e-mail: willem.wamsteker@esa.int
³ Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA e-mail: nagy@mathcs.emory.edu
⁴ Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden CO 80401, USA e-mail: ltenorio@Mines.EDU

Corresponding author: R. Vio, robertovio@tin.it

Received: 8 September 2003
Accepted: 19 November 2003

Abstract

We consider the simultaneous deblurring of a set of noisy images whose point spread functions are different but known and spatially invariant, and with Gaussian noise. Currently available iterative algorithms that are typically used for this type of problem are computationally expensive, which makes their application for very large images impractical. We present a simple extension of a classical least-squares (LS) method where the multi-image deblurring is efficiently reduced to a computationally efficient single-image deblurring. In particular, we show that it is possible to remarkably improve the ill-conditioning of the LS problem by means of stable operations on the corresponding normal equations, which in turn speed up the convergence rate of the iterative algorithms. The performance and limitations of the method are analyzed through numerical simulations. Its connection with a column weighted least-squares approach is also considered in an appendix.