Distributed processing in frames for sparse approximation

Beyond signal processing applications, frames are also powerful tools for modeling the sensing and information processing of many biological and man-made systems that exhibit inherent redundancy. In many cases, these systems are required to use distributed computational strategies to analyze and process the sensory information. In this talk, I will review the use of frames to model distributed sensing systems with a particular focus on sensory neural systems. In light of the evidence that many of these systems employ sparse codes, I will describe our Locally Competitive Algorithms (LCAs) that use a dynamical system to solve many sparse approximation problems. These LCAs employ a parallel computational architecture with simple analog components. I will show numerical simulation results for these systems and describe their relationship to the many recently-proposed iterative thresholding algorithms. Our LCA approach also demonstrates potential advantages in coding time-varying signals (e.g., video) by reflecting the smooth signal changes in smooth coefficient variations. Finally, I will highlight some future directions where we hope to impact areas such as efficient analog signal processing devices, fast discrete approximation algorithms, and video processing and computer vision in complex temporal environments.