Ill-posedness of space-variant image deconvolution

Michael Kieweg; Herbert Gross; Torsten Sievers; Lothar Müller

doi:10.1117/12.858259

25 August 2010 Ill-posedness of space-variant image deconvolution

Michael Kieweg, Herbert Gross, Torsten Sievers, Lothar Müller

Proceedings Volume 7800, Image Reconstruction from Incomplete Data VI; 78000K (2010) https://doi.org/10.1117/12.858259
Event: SPIE Optical Engineering + Applications, 2010, San Diego, California, United States

Abstract

In optical systems with quite good correction, the field-dependence of aberrations often can be neglected. In low performance systems, for the application of deconvolution methods the field-dependence of the point spread function must be taken into account. However, the number of publications dealing with the topic of space-variant deconvolution in order to compensate system aberrations is quite low. In this contribution, we investigate the fundamental difficulty accompanied by space-variant deconvolution, which makes the problem ill-posed, even in the case of non-vanishing modular transfer functions and the assumption of noise-free imaging. The spatial frequencies of the image spectrum are mixed depending on the field-dependencies of the optical aberrations. In general, it is therefore not possible to reconstruct the individual frequencies exactly. Some discrete examples with a non unique solution are presented. For the 2D case, we will show and investigate how the most popular algorithms deal with this fundamental problem for different typical types of optical aberrations. Depending on the aberration, the computational results for those algorithms differ from very good results to images with artifacts. The Lucy Richardson method, which is often recommended in the case of spaceinvariant image reconstruction since it may even reconstruct frequencies above the cut off frequency, provides poor results for unsymmetrical space-variant aberrations like Coma or a simple Tilt. However, we will show that a simpler method like the Landweber algorithm is better suited to deal with those kinds of aberrations.

Citation Download Citation

Michael Kieweg, Herbert Gross, Torsten Sievers, and Lothar Müller "Ill-posedness of space-variant image deconvolution", Proc. SPIE 7800, Image Reconstruction from Incomplete Data VI, 78000K (25 August 2010); https://doi.org/10.1117/12.858259

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