Deblurring space-variant blur by adding noisy image

Abstract

Imaging restoration is an essential step in hybrid optical and image processing system which relays on poor optics. The poor optics makes the blur ill-conditioned and turns the deblurring process difficult and unstable. Recently the idea of parallel optics (PO) was introduced. In the parallel optics setup the optical system is composed of a main system and an auxiliary system. The auxiliary system is designed to improve the stability of the deblurring process by improving the condition number of the blurring operator. In this paper we show that in one such system the post processing acts as a noise filter hence allows to work with noisy data in the auxiliary channel. Using the singular value decomposition we derive analytical limit for the difference in SNR requirements of the auxiliary channel relative to that of the main channel. The gap between the SNR requirements of the two systems is analyzed theoretically and proved to be as large as 27.68 [db]. Image restoration comparison on simulations is performed between a blurred/noisy pair with average SNR gap of 20 [db] and a system without an auxiliary system. The average Mean Square Error Improvement Factor (MSEIF) achieved by the blurred/noisy pair, was 13.9 [db] higher than the system without a noisy auxiliary system. © 2012 Springer-Verlag.