A new construction of compressed sensing matrices for signal processing via vector spaces over finite fields
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As an emerging sampling technique, Compressed Sensing provides a quite masterly approach to data acquisition. Compared with the traditional method, how to conquer the Shannon/Nyquist sampling theorem has been fundamentally resolved. In this paper, first, we provide deterministic constructions of sensing matrices based on vector spaces over finite fields. Second, we analyze two kinds of attributes of sensing matrices. One is the recovery performance with respect to compressing and recovering signals in terms of restricted isometry property. In particular, we obtain a series of binary sensing matrices with sparsity level that are quite better than some existing ones. In order to save the storage space and accelerate the recovery process of signals, another character sparsity of matrices has been taken into account. Third, we merge our binary matrices with some matrices owning low coherence in terms of an embedding manipulation to obtain the improved matrices still having low coherence. Finally, compared with the quintessential binary matrices, the improved matrices possess better character of compressing and recovering signals. The favorable performance of our binary and improved matrices have been demonstrated by numerical simulations.
KeywordsCompressed sensing matrices Vector spaces Coherence Restricted isometry property Signal processing
This paper is supported by the National Natural Science Foundation of China under grant No. 61501080, 61572095, 61871064, 61877007, 61771090, the Fundamental Research Funds for the Central Universities under No. DUT19JC08, and the Guangxi Key Laboratory of Trusted Software under No. kx201903.
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