Blind deconvolution using a normalized sparsity measure

TLDR

Blind image deconvolution is ill‑posed, and common image priors often fail to recover the true sharp image, necessitating additional methods such as Bayesian approaches or edge‑localization techniques. This paper introduces a new regularization that assigns the lowest cost to the true sharp image. The regularization enables a simple cost formulation that eliminates the need for extra methods, and the algorithm is demonstrated on real images with both spatially invariant and varying blur. Because of its simplicity, the algorithm is fast and highly robust.

Abstract

Blind image deconvolution is an ill-posed problem that requires regularization to solve. However, many common forms of image prior used in this setting have a major drawback in that the minimum of the resulting cost function does not correspond to the true sharp solution. Accordingly, a range of additional methods are needed to yield good results (Bayesian methods, adaptive cost functions, alpha-matte extraction and edge localization). In this paper we introduce a new type of image regularization which gives lowest cost for the true sharp image. This allows a very simple cost formulation to be used for the blind deconvolution model, obviating the need for additional methods. Due to its simplicity the algorithm is fast and very robust. We demonstrate our method on real images with both spatially invariant and spatially varying blur.