Sparse Encoding of Signals through Structured Random Sampling
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Abstract: The novel paradigm of compressive-sensing (CS), which aims to achieve simultaneous acquisition and compression of signals, has received significant interest in recent years. Several CS-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 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. 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, which 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 predefined structure in the sampling-pattern can be further exploited to design fast recovery algorithms. The main theme is to develop algorithms that bridge the gap between theory and practice of random sampling. The work is motivated by several application problems where structured random sampling offers attractive solutions.