Sparse Encoding of Signals through Structured Random Sampling.

Abstract

The novel paradigm of compressive sampling/sensing (CS), which aims to achieve simultaneous acquisition and compression of signals, has received significant research interest in recent years. CS has been widely applied in many areas and several novel algorithms have been developed over the past few years. However, practical implementation of CS systems remains somewhat limited. This is due to the limited scope of many algorithms in literature when it comes to the employed measurement architectures. In several CS techniques, a key problem is that physical constraints typically make it infeasible to actually implement many of the random projections described in the algorithms. Also, most methods focus only on discrete measurements of the signal, which is not always practicable. Therefore, innovative and practical sampling systems must be carefully designed to effectively exploit CS theory in practice. This work focuses on developing techniques that randomly sample in time, that are also characterized by the presence of some structure in the sampling pattern. The structure is leveraged to enable a feasible implementation of acquisition hardware, while the randomness ensures recovery of sparse signals via greedy pursuit algorithms. In certain cases, the presence of a predefined structure in the sampling pattern can be further exploited to obtain other advantages such as reducing the run-time of reconstruction algorithms.

The main theme in the thesis is to develop algorithms that bridge the gap between theory and practice of structured random sampling. The work is motivated by several application problems where structured random sampling offers attractive solutions. One of the applications involves development of a low-power architecture for analog-to-digital conversion (ADC), that incorporates time-domain processing and random sampling techniques, improving energy efficiency in both ways. Similar techniques in structured random sampling are employed to develop a novel low-rate neuron model which encodes information present in sensory stimuli at a rate that is proportional to the actual amount of information present in the signal rather than its duration. Along with techniques borrowed from theoretical computer science, structured random sampling has been successfully employed in designing a novel, distributive, spectrum sensing scheme for application in wide-band cognitive radios.