Low Power Sparse Approximation on Reconfigurable Analog Hardware

Compressed sensing is an important application in signal and image processing which requires solving nonlinear optimization problems. A Hopfield-Network-like analog system is proposed as a solution, using the locally competitive algorithm (LCA) to solve an overcomplete l₁ sparse approximation problem. A scalable system architecture using sub-threshold currents is described, including vector matrix multipliers (VMMs) and a nonlinear thresholder. A 4 × 6 nonlinear system is implemented on the RASP 2.9v chip, a field programmable analog array with directly programmable floating gate elements, allowing highly accurate VMMs. The circuit successfully reproduced the outputs of a digital optimization program, converging to within 4.8% rms, and an objective value only 1.3% higher on average. The active circuit consumed 29 μA of current at 2.4 V, and converges on solutions in 240 μs. A smaller 2 × 3 system is also implemented. Extrapolating the scaling trends to a N=1000 node system, the analog LCA compares favorably with state-of-the-art digital solutions, using a small fraction of the power to arrive at solutions ten times faster. Finally, we provide simulations of large scale systems to show the behavior of the system scaled to nontrivial problem sizes.