Compressed sensing reconstruction of sparse spectrum based on digital micro-mirror device platform

Abstract

A new method which employs compressive sensing (CS) to reconstruct the sparse spectrum is designed and experimentally demonstrated. On the basis of CS theory, the simulation results indicate that the probability of reconstruction is high when the step of the sparsity adaptive matching pursuit algorithm is confirmed as 1. Contrastive analysis for four kinds of commonly used measurement matrices: part Hadamard, Bernoulli, Toeplitz and Circular matrix, has been conducted. The results illustrate that the part Hadamard matrix has better performance of reconstruction than the other matrices. The experimental system of the spectral compression reconstruction is mainly based on the digital micro-mirror device (DMD). The experimental results prove that CS can reconstruct sparse spectrum well under the condition of 50% sampling rate. The system error 0.078 1 is obtained, which is defined by the average value of the 2-norm. Furthermore, the proposed method shows a dominant ability to discard redundancy.

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