Sparse sampling and signal compressive sensing reconstruction method

Abstract

The invention discloses a sparse sampling and signal compressive sensing reconstruction method. The method comprises: establishing a signal sampling interval of each time, sampling point number, and the number of points recovering, establishing random sparse sampling lower than a Nyquist sampling theorem value; and designing a measurement matrix by random sampling timing sequence values, designing a transformation matrix of a sparse expression domain of signals, determining a compressive sensing matrix, and separated compressive sensing optimizing signal reconstruction in a nonlinear manner. The method is based on rationality of objective world rules, and makes full use of signal sparsity, uses transformation space to describe the signals, and establishes theoretical framework of new signal description and processing, so under the condition that information is not lost is ensured, signals are sampled by speed much lower than required speed of a Shannon's sampling theorem. Simultaneously, signals can be recovered completely, that is, sampling of signals is converted into sampling of information. The invention provides a whole set of complete method. The method can be used in one-dimensional and multidimensional signals, and can process audio frequency, videos, nuclear magnetic resonance, and other signals.

Description

technical field [0001] The invention belongs to the technical field of signal processing, in particular to a sparse sampling and signal compression sensing reconstruction method. Background technique [0002] Classical data compression technology, whether it is audio compression (such as mp3), image compression (such as jpeg), video compression (mpeg), or general coding compression (zip), is based on the characteristics of the data itself, looking for and removing data The implicit redundancy in the , so as to achieve the purpose of compression. Such compression has two characteristics: first, it occurs after the data has been completely collected; second, it requires complex algorithms to complete. In contrast, the decoding process is generally relatively simple in calculation. Taking audio compression as an example, the calculation amount of compressing an mp3 file is much greater than the calculation amount of playing (ie decompressing) an mp3 file; [0003] This asymme...

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Problems solved by technology

[0006] There are two defects in the above theory: (1) Since the sampling rate of the signal must not be lower than twice the signal bandwidth (the difference between the highest frequency and the lowest frequency of the signal), this The hardware system is under great pressure on the sampling rate; (2) In the process of compression encoding, in order to reduce the cost of storage, processing and transmission, a large number of small coefficients obtained by transform calculations are discarded, resulting in data calculation and memory resources. waste

This high-speed sampling and recompression process wastes a lot of sampling resources, so it naturally leads to a question: whether other transformation spaces can be used to describe signals, and a new theoretical framework for signal description and processing can be established, so that information can be guaranteed without loss. In this case, the signal is sampled at a rate much lower than that required by Shannon's sampling theorem, while fully recovering the signal

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