Graph Spectral Compressed Sensing

This report focuses on the theoretical analysis of Compressed Sensing(CS) with the partial Graph Fourier ensemble sensing matrix. In this report, we prove that with the help of additional knowledge of a linear compressible signal, a stable recovery can still be guaranteed even if the entries of the orthogonal sensing matrix is not uniformly bounded. More specifically, we construct a sensing matrix by randomly select a certain number of the rows from the graph Laplacian eigenbasis matrix. It is shown in this report that if the signal is smooth on the graph which satisfies certain conditions, we can still utilize `1 decoding to reconstruct the original signal.

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