Blind image deconvolution based on sparsity: Theoretical justification and improvement of state-of-the-art techniques
Observed signals and images are distorted by noise and blurring. In precise terms, blurring is a convolution of the original image with some blurring function. From this viewpoint, to reconstruct the original image, we need to reverse the effects of this convolution, i.e., to “deconvolve” the image.^ Many efficient methods for image deconvolution are known. However, most of these methods assume that we know the blurring function -- or at least that we have some partial information about the blurring function. In some practical situations, however, we do not have this information. In such situations, we need to perform, blind image deconvolution, i.e., deconvolution without any knowledge about the original blurring function.^ Recently, several algorithms have been proposed that successfully perform blind image deconvolution. However, these algorithms have some limitations. First, some of the techniques used by these algorithms lack a convincing theoretical justification. Without a theoretical justification, there is no guarantee that these methods will be as successful on other images as they are on currently tested examples. Second, these methods are still not perfect, so it is desirable to try tot improve them.^ In this dissertation, we start with the state-of-the-art blind image deconvolution method based on the ideas of sparsity and lp -regularization – ideas which do not have a convincing theoretical justification. We provide a theoretical justification for these ideas, and we also describe a modification of the state-of-the-art techniques that lead to a better quality blind image deconvolution.^
Cervantes, Fernando, "Blind image deconvolution based on sparsity: Theoretical justification and improvement of state-of-the-art techniques" (2016). ETD Collection for University of Texas, El Paso. AAI10151170.