Modern techniques giving the best performance for acquiring and processing signals/images rely on repeatedly solving mathematical optimization problems which can be computationally expensive. This research involves advancing, by orders of magnitude, the state of the art for solving an important class of these problems. Rather than developing algorithms tailored to current digital computational platform, the investigators depart completely from this current line of research to study analog architectures for solving these problems. These analog architectures, when fully developed, have the potential for dramatic gains in speed and power efficiency over their digital counterparts. This research project is inherently multidisciplinary, as it combines recent advances in computational neuroscience, signal processing, and reconfigurable VLSI architectures. Among other applications, these systems enable reductions in the time needed to acquire a magnetic resonance image (MRI).
This project focuses primarily on solving optimization programs combining a mean-squared error data fidelity term with a sparsity inducing cost function (e.g., the L1 norm) via an analog dynamical system architecture. Specifically , the project contains two intertwined threads: circuit implementation and mathematical analysis. The goal of the circuit implementation thread is to produce a analog circuit which solves significant optimization programs (e.g., tens of thousands of variables) substantially faster than state-of-the-art digital solutions. The investigators leverage recent advances in reconfigurable analog architectures to achieve efficient designs at this large scale. The analysis thread includes deriving bounds on the circuit convergence time and generalizing the architecture to include other relevant signal processing problems. The research also involves applying this analog architecture as a nonlinear "filter" which continuously reacts to changes in the input.
