Advisor:  Dr. Margaret CheneyCo-Advisor:Dr. Raghu Raj

Committee:  Dr. Emily King, Dr. Mahmood Azimi-Sadjadi

Title: Deep Compound Gaussian Prior for Linear Inverse Problems

Abstract: Linear inverse problems are common in a variety of areas including compressive sensing and image reconstruction, which have applications in 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 least squares problem. Data-driven methods learn the inverse reconstruction mapping directly by training a neural network structure on actual signals and signal measurements. 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. The performance of unrolled DNNs often exceeds that of corresponding iterative algorithms and standard DNNs and does so in a computationally efficient fashion. In this work, we leverage algorithm unrolling to combine a powerful statistical prior, the Compound Gaussian prior, with the powerful representational ability of machine learning and DNN approaches.

Specifically, we construct a Compound Gaussian inspired, regularized least squares iterative image reconstruction algorithm and provide a computational theory for this algorithm.

Furthermore, we apply algorithm unrolling in two distinct techniques:

one provides a learning for the geometry of the optimization landscape and a second provides partial learning of the prior distribution within the Compound Gaussian family. Simulation results show our unrolled DNNs outperform state-of-the-art iterative imaging algorithms and recent deep learning based approaches.

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Meeting ID: 979 2293 0774

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