Random Sparse Sampling and Equal Intervals Bregman High-Resolution Signal Reconstruction

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Qin, Guojun; Wang, Jingfang

Random Sparse Sampling and Equal Intervals Bregman High-Resolution Signal Reconstruction Journal Article

Mechanics, Materials Science & Engineering, 11 , 2017, ISSN: 2412-5954.

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Authors: Guojun Qin, Jingfang Wang

ABSTRACT. Compressed sensing (CS) is a new signal processing methods, signal sampling and reconstruction are processed to take full advantage of the signal sparse knowledge structure in the transform domain. It consists of three elements: the sparse matrix, incoherent measurement matrix and reconstruction algorithm. In the framework of compressed sensing theory, the sampling rate is no longer decided in the bandwidth of the signal, but it depends on the structure and content of the information in the signal. In this paper, a complex domain random observation matrix is designed and interval samples are projected to any set of random sample, ie, sparse random sampling. The signal is successfully restored by the use of Bregman algorithm. The signal is described in the transform space, and a theoretical framework is established with a new signal descriptions and processing. By making the case to ensure that the information loss, signal is sampled at much lower than the Nyquist sampling theorem requiring rate, but also the signal is completely restored in high probability. The sparse signal is simulated in sampling and reconstruction of time domain and frequency domain, and the signal length, the measured value, the signal sparse level and SNR influence are analyzed in the reconstruction error.

Keywords: compressed sensing, random sampling, incoherent measurement matrix, sparse sampling, Bregman reconstruction

DOI 10.2412/mmse.74.23.960

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