|M.Sc Student||Bronstein Alexander|
|Subject||Blind Deconvolution using Relative Newton Algorithm and|
Learnable Sparse Representations
|Department||Department of Electrical Engineering||Supervisors||Dr. Michael Zibulevsky|
|Professor Emeritus Yehoshua Zeevi|
The need to restore a signal degraded by an unknown convolutional system appears in a variety of fields. The past few decades gave rise to two very distinct ``cultures" of blind deconvolution. On one hand, there exist numerous blind channel equalization algorithms used mainly in communications, which achieve low computational complexity by imposing very restricting assumptions on the source signals. On the other hand, the image processing community offers universal, yet slow methods for restoration of natural images. A common denominator of these two worlds is almost absent, due to the very different nature of the signals of interest.
This thesis presents an attempt to bridge the two domains. In the first part, we adopt the quasi-maximum-likelihood (QML) framework used by several state-of-the-art blind deconvolution methods, and propose an efficient Newton-based iterative optimization algorithm, which improves both accuracy and convergence speed, maintaining comparable iteration complexity. We propose the use of ARMA-parameterized restoration kernels, which constitute a richer family of filters than the traditionally-used FIR filters. We also present a theoretical analysis, which allows to predict the restoration quality.
In the second part, we present a supervised learning approach of optimal sparse representations, which allow to shrink a diversity of images and their properties into a universal sparsity prior. This makes possible the use of efficient QML-based numerical tools for blind deconvolution of natural images that usually do not admit the restrictive assumptions of this framework. We show that our approach allows construction of learnable priors. This approach generalizes several classical studies in image deconvolution such as the total variation deconvolution. Lastly, we discuss the generalization of the proposed methods to the multichannel and the complex cases.