Image Restoration with Multiple Hard Constraints on Data-Fidelity to Blurred/Noisy Image Pair

Existing image deblurring methods with a blurred/noisy image pair take a two-step approach: blur kernel estimation and image restoration. They can achieve better and much more stable blur kernel estimation than single image deblurring methods. On the other hand, in the image restoration step, they do not exploit the information on the noisy image, or they require ad hoc tuning of interdependent parameters. This paper focuses on the image restoration step and proposes a new restoration method of using a blurred/noisy image pair. In our method, the image restoration problem is formulated as a constrained convex optimization problem, where data-fidelity to a blurred image and that to a noisy image is properly taken into account as multiple hard constraints. This offers (i) high quality restoration when the blurred image also contains noise; (ii) robustness to the estimation error of the blur kernel; and (iii) easy parameter setting. We also provide an efficient algorithm for solving our optimization problem based on the so-called alternating direction method of multipliers (ADMM). Experimental results support our claims.