CIF: Small: Blind Perfect Signal Reconstruction in Subsampled Multi-Channel Systems

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Multi-channel systems arise whenever a signal is picked up in or sent to more than one location. They are ubiquitous in imaging and sensing, data communication and storage, and in all audio, speech, or image processing digital technologies. Their applications range from ultrasound or MRI diagnostic scanners, to radio astronomy. The rich theory of multi-channel systems addresses two scenarios: when the entire system, including the channels, can be freely designed; or when the channels may be fixed and unknown, but data at the output of each channel is fully acquired. However, in many important applications this is not the case. The characteristics of the channels are often dictated by the physics governing the sensing process, which are unknown because of interaction of the sensors with the environment or their miss-calibration. Furthermore, because of physical or cost constraints only partial (subsampled) channel data is available. The goal of this project is to develop, evaluate and demonstrate the fundamental theory and design tools to address this important class of problems. This project aims to extend the methods of blind multi-channel deconvolution, which are currently limited to non-subsampled systems , to provide blind perfect signal reconstruction from subsampled data. The specific aims of this project are to: (1) develop the theory of blind identification of subsampled multi-channel systems; (2) propose practical methods for blind identification of such systems using perfect (or near perfect) reconstruction filter banks; (3) provide analytical tools to study and quantify various tradeoffs between conditioning (noise performance), signal distortion, robustness, and computational cost; and (4) to demonstrate performance gains on real applications, and in particular in highly-accelerated multi-channel magnetic resonance imaging (MRI), and robust image super-resolution.