A Stochastic Relaxed Energy Model for Image Deblurring

• Activity Number: 655
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Walid Sharabati*+ and Mohamed El-Gebeily
• Companies: Purdue University and KFUPM
• Keywords: Relaxed energy ; Image reconstruction ; Stochastic Banach space ; Half-quadratic approximation ; KL-expansion ; Tikhonov regularization

Abstract

Image processing deals with blurriness and noise generated when the lens is out of focus, incoming light is bent, or object moves while shutter is open. We develop a relaxed energy model based on Tikhonov regularization with random parameters to deblur images, the optimizer produces a stochastic nonlinear system of integro-differential equations. In the first step, we introduce stochastic Banach spaces suitable for the problem and then discuss existence, uniqueness, convergence and stability of the stochastic solution as well as the variational formulation, we show that the approximated relaxed energy has a unique minimizer. Because the problem is highly nonlinear and numerical computations are cumbersome we implement the half-quadratic approximation and incorporate the Karhunen-Loeve spectral expansion to eliminate the dependency on the random effect. The problem is then discretized with respect to the deterministic and probabilistic finite-dimensional subspaces.