Simultaneous Depth Recovery and Image Restoration

Abstract

Given an image degraded by a linear space-variant (LSV) blur, the problem of restoring the original image is an interesting and challenging task. Space-variant image restoration is a problem of considerable importance in image processing because in realworld situations, the degradations are often space-varying. In comparison to the amount of work done on linear space-invariant image restoration [KT91,ST90], the literature records only a few results on the restoration of images degraded by LSV blurs. In [RH72], Robbins and Huang proposed an inversion procedure for LSV image restoration based on the Mellin transform. Sawchuk [Saw74] converted the spatially varying problem to a spatially invariant one using a suitable coordinate transformation. The approach is applicable to only a special class of LSV degradations that can be transformed into a linear space invariant (LSI) degradation. Frieden [Fri72] developed a restoration formula based on the principle of maximum entropy. In [AJ78], Angel and Jain employ a conjugate gradient descent method for restoration of images degraded by spatially varying PSFs. Trussel et al. propose a method in which the image is partitioned into rectangular regions, and each region is restored using a space-invariant technique, such as the MAP filter TH78a, TH78b] or the modified Landweber filter [TF92]. In [RR81], Schafer et al. present an iterative method for LSV image restoration. In [AS93], Patti et al. apply the reduced order Kalman filter for space-variant image restoration. The approach, however, has been found to be computationally expensive even for a moderate blur size. Ozkan et al. [MS94] propose the use of projections onto convex sets for space-varying image restoration. The method uses a set of deconvolution constraints that allow the use of a different PSF at each pixel. In [SB95], Koch et al. propose a multiple model-based extended Kalman filter for restoration of spatially varying blurred images. Note that in all the above methods, the space-variant blur is assumed to be known.