Image Deblurring with Compressive Sensing

Abstract

Compressive sensing is a technique that enables recovery of signals represented by an underdetermined system of equations. Such a recovery of an original signal is made possible if the samples are represented in a sparse manner provided an appropriate measuring matrix is used for the modelled system. Blurred images are examples of signals that are sparse especially in transform domains. Different researches have been done to show the possibility of recovering blurred images that use sparse representation of transform domains by applying compressive sensing. In our work, however, we propose a model that doesn’t require transforming into other domains. In addition, a box-wise approach has been used that derives the underdetermined system matrix from 7x7 segmented boxes of the blurred image. Compressive sensing algorithms are applied on these boxes to recover the whole image iteratively. Our method is shown to have a much better computational complexity than the traditional Lucy-Richardson deblurring method. Thus, with this improved computational complexity, the study provides an initial platform to deblur images using box-wise method and compressive sensing technique.