Edge preserving image restoration using convex optimization

Restoring an original image from its blurred and noisy version is usually ill-posed. l₂ norm based regularized inverse solutions lead to restored images with the edges blurred. Some work has focused on using the l₁ norm of the gradient as a regularizer. Alternatively convex optimization approaches have been used to provide flexibility to impose multiple constraints on the solution. In this paper, we combine these methods using a convex optimization approach based on the ellipsoid algorithm to impose, among other constraints, an l₁ norm of the gradient constraint. This results in a restored image with good edge preservation capabilities