Join Zoom Meeting: https://zoom.us/j/96726281191?pwd=KzhjL2FJd0FsNk9yamdNK0c4Tng0QT09
Meeting ID: 967 2628 1191
Passcode: 389051

Advisor:  Dr. Margaret Cheney          Co-Advisor:  Raghu Raj    Committee:  Dr. Jennifer Mueller, Dr. Emily King, Dr. Mahmood Azimi-Sadjadi

Title:  Compound-Gaussian-Regularized Inverse Problems: Theory, Algorithms, and Neural Networks

Abstract:   Linear inverse problems are common in a variety of areas including compressive sensing, radar, sonar, medical, and tomographic imaging. Model-based and data-driven methods are two prevalent classes of approaches to solve linear inverse problems. Model-based methods incorporate certain assumptions, such as the image prior distribution, into an iterative estimation algorithm often, as an example, solving a regularized least squares problem. Instead, data-driven methods learn the inverse reconstruction mapping directly by training a neural network structure on actual signals and signal measurement pairs. Alternatively, algorithm unrolling, a recent approach to linear inverse problems, combines the model-based and data-driven methods through the implementation of an iterative estimation algorithm as a deep neural network (DNN). This approach offers a vehicle to embed domain-level and algorithmic insights into the design of networks in a way that makes the network layers interpretable. In this work, we leverage algorithm unrolling to combine a powerful statistical prior, the Compound Gaussian (CG) prior, with the powerful representational ability of machine learning and DNN approaches. Specifically, a general CG-based iterative algorithm is presented and unrolled to create a class of CG-based DNNs. Two particular instances of this class are thoroughly analyzed theoretically on convergence and empirically on tomographic imaging and compressive sensing problems, which shows that our CG-based approaches outperform state-of-the-art iterative imaging algorithms as well as recent deep learning approaches. Finally, a generalization error bound on our class of CG-based DNNs is discussed and applied to the two particular instances of the class.