Processing Blurred Images with Random Data

• Activity Number: 693
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Walid Sharabati*+ and Mohamed Al-Gebeily
• Companies: KFUPM and King Fahd University of Petroleum and Minerals
• Keywords: Image Deblurring ; Stochastic Smoothing Operator ; Euler-Lagrange Equations ; Image Reconstruction ; Total Variation ; KL Expansion

Abstract

The objective of image deblurring is to reduce the noise generated when the lens is out of focus, incoming light is bent, or object moves while shutter is open. In this work, we present an abstract analysis of Euler-Lagrange equations associated with the total variation model based on Tikhonov regularization with random input data to reconstruct the original image. The optimizer produces a nonlinear system of elliptic type equations. To this end, we introduce a stochastic smoothing operator and develop a stochastic version of the Euler-Lagrange equations defined on suitable finite dimensional deterministic and probability spaces. We incorporate spectral expansion techniques such as the KL expansion to eliminate the dependency on the random effect.