Greedy Algorithms for Distributed Compressed Sensing

Abstract: Compressed sensing (CS) is a recently invented sub-sampling technique that utilizes sparsity in full signals. Most natural signals possess this sparsity property. From a sub-sampled vector, some CS reconstruction algorithm is used to recover the full signal. One class of reconstruction algorithms is formed by the greedy pursuit, or simply greedy, algorithms, which is popular due to low complexity and good performance. Meanwhile, in sensor networks, sensor nodes monitor natural data for estimation or detection. One application of sensor networking is in cognitive radio networks, where sensor nodes want to estimate a power spectral density. The data measured by different sensors in such networks are typically correlated. Another type are multiple processor networks of computational nodes that cooperate to solve problems too difficult for the nodes to solve individually.In this thesis, we mainly consider greedy algorithms for distributed CS. To this end, we begin with a review of current knowledge in the field. Here, we also introduce signal models to model correlation and network models for simulation of network. We proceed by considering two applications; power spectrum density estimation and distributed reconstruction algorithms for multiple processor networks. Then, we delve deeper into the greedy algorithms with the objective to improve reconstruction performance; this naturally comes at the expense of increased computational complexity. The main objective of the thesis is to design greedy algorithms for distributed CS that exploit data correlation in sensor networks to improve performance. We develop several such algorithms, where a key element is to use intuitive democratic voting principles. Finally, we show the merit of such voting principles by probabilistic analysis based on a new input/output system model of greedy algorithms in CS.By comparing the new single sensor algorithms to well known greedy pursuit algorithms already present in the literature, we see that the goal of improved performance is achieved. We compare complexity using big-O analysis where the increased complexity is characterized. Using simulations we verify the performance and confirm complexity claims. The complexity of distributed algorithms is typically harder to analyze since it depends on the specific problem and network topology. However, when analysis is not possible, we provide extensive simulation results. No distributed algorithms based on the signal-models used in this thesis were so far available in the literature. Therefore, we compare our algorithms to standard single-sensor algorithms, and our results can then easily be used as benchmarks for future research. Compared to the stand-alone case, the new distributed algorithms provide significant performance gains. Throughout the thesis, we strive to present the work in a smooth flow of algorithm design, simulation results and analysis.