Open Access
Seyed Mousavi, Hojjat
Graduate Program:
Electrical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
August 16, 2017
Committee Members:
  • Vishal Monga, Dissertation Advisor
  • Vishal Monga, Committee Chair
  • Robert Collins, Committee Member
  • Constantino Manuel Lagoa, Committee Member
  • William Evan Higgins, Outside Member
  • image proccessing
  • signal processing
  • super resolution
  • deep learning
  • sparse coding
  • sparssity
  • optimization
  • convex
Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown signi cant improvement in real-world applications such as recovery, classi cation, clustering, super resolution, etc. This vast influence of sparse signal processing in real-world problems raises a signi cant need in developing novel sparse signal representation algorithms to obtain more robust systems. In such algorithms, a few open challenges remain in (a) efficiently posing sparsity on signals that can capture the structure of underlying signal and (b) the design of tractable algorithms that can recover signals under aforementioned sparse models. In this dissertation, we try to view the signal recovery problem from these viewpoints. First, we address the sparse signal recovery problem from a Bayesian perspective where sparsity is enforced on reconstruction coefficients via probabilistic priors. In particular, we focus on a variant of spike and slab prior, which is known to be the gold standard to encourage sparsity. The optimization problem resulting from this model has broad applicability in recovery and regression problems and is known to be a hard non-convex problem whose existing solutions involve simplifying assumptions and/or relaxations. We propose an approach called Iterative Convex Refi nement (ICR) that aims to solve the aforementioned optimization problem directly allowing for greater generality in the sparse structure. Essentially, ICR solves a sequence of convex optimization problems such that sequence of solutions converges to a sub-optimal solution of the original hard optimization problem. We propose two versions of our algorithm: (a) an unconstrained version, and (b) with a non-negativity constraint on sparse coefficients, which may be required in some real-world problems. Many signal processing problems in computer vision and recognition world can bene t from ICR. These include face recognition in surveillance applications, object detection and classi cation in the video, image compression and recovery, image quality enhancement etc. On the other hand, one of the most signi cant challenges in image processing is the enhancement of image quality. To address this challenge we aim to recover signals by using the prior structural knowledge about them. In particular, we pose physically meaningful probabilistic priors to promote sparsity on reconstruction coefficients or design parameters of the problem. This has a variety of applications in signal and image processing including but not limited to regression, denoising, inverse problems, demosaicking and super-resolution. In particular, sparsity constrained single image super-resolution (SR) has been of much recent interest. A typical approach involves sparsely representing patches in a low resolution input image via a dictionary of example LR patches, and then using the coecients of this representation to generate the high-resolution output via an analogous HR dictionary. In this dissertation, we propose extension of the SR problem which is twofold: (1) extension of sparsity-based SR problems to multiple color channels by taking prior knowledge about the color information into account. Edge similarities amongst RGB color bands are exploited as cross-channel correlation constraints. These additional constraints lead to a new optimization problem, which is not easily solvable; however, a tractable solution is proposed to solve it efficiently. Moreover, to fully exploit the complementary information among color channels, a dictionary learning method is also proposed speci cally to learn color dictionaries that encourage edge similarities (2) Tackle the super-resolution problem from a deep learning standpoint and provide deep network structures designed for superresolution. A step further in this line of research is to integrate sparsifying priors into deep networks and investigate their impact on the performance especially in absence of abundant training.