Construction of compressed sensing matrices for signal processing

To cope with the huge expenditure associated with the fast growing sampling rate, compressed sensing (CS) is proposed as an effective technique of signal processing. In this paper, first, we construct a type of CS matrix to process signals based on singular linear spaces over finite fields. Second, we analyze two kinds of attributes of sensing matrices. One is the recovery performance corresponding to compressing and recovering signals. In particular, we apply two types of criteria, error-correcting pooling designs (PD) and restricted isometry property (RIP), to investigate this attribute. Another is the sparsity corresponding to storage and transmission signals. Third, in order to improve the ability associated with our matrices, we use an embedding approach to merge our binary matrices with some other matrices owing low coherence. At last, we compare our matrices with other existing ones via numerical simulations and the results show that ours outperform others.

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