Optimal compressive sensing systems for signal acquisition, reconstruction and processing

点击翻译按钮获取中文摘要

In a nutshell, a compressive sensing (CS) system acquires a signal of interest indirectly by correcting a small number of its "projections" rather than evenly sampling it at the so-called Nyquist rate which can be prohibitively high for broadband signals encountered in many applications. This new signal acquisition paradigm has revolutionized the way digital data are traditionally acquired. The objectives of the proposed research are threefold. First, we aim at developing optimal CS systems that require fewer-than-ever number of measurements that yet contain complete information of the data. This entails reduced number of sensing devices (or lower software complexity in the case of software implementation), hence improving processing efficiency and reducing cost. This goal will be achieved by exploring and maximizing a new measure for the incoherence between the measurement subsystem and an overcomplete dictionary for sparse representation of signals. Second, we investigate new methods to recover the data of interest from the limited number of measurements with better accuracy relative to existing algorithms. Our interest is in large-scale data, hence we must develop fast algorithms for them to be useful in real-time data processing. To this end, we shall develop a class of proximal-gradient algorithms for solving Lp type (with p < 1) mixed convex-nonconvex problems. Third, the algorithms developed are to be applied to problems in digital signal processing such as de- nosing, de-blurring and segmentation in medical imaging and communications such as wireless channel estimation and message recovery problems. These problems are current, significant and technically challenging in their respective fields either because of their involvement in large amount of data (medical imaging) or because of their real-time nature (wireless communication applications). The information processing communities will regard our research endeavors as significant when the proposed algorithms begin to play a crucial role in solving these and other related problems with satisfactory processing speed and performance.