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Compressed sensing observation matrix constructing method based on sparse Hadamard matrix

A technology of observation matrix and construction method, applied in electrical components, code conversion, etc., can solve the problems of high hardware support, high hardware cost, and high computational complexity, and achieve easy hardware implementation, low hardware requirements, and reduced computational complexity. Effect

Active Publication Date: 2012-02-15
TSINGHUA UNIV +1
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Problems solved by technology

[0005] However, the disadvantage of the existing observation matrix is ​​that the computational complexity of the compressed sampling and reconstruction recovery of the data is high through the existing observation matrix
In addition, the existing observation matrix has relatively high hardware support, which is not conducive to the realization of hardware, resulting in high hardware cost

Method used

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  • Compressed sensing observation matrix constructing method based on sparse Hadamard matrix
  • Compressed sensing observation matrix constructing method based on sparse Hadamard matrix
  • Compressed sensing observation matrix constructing method based on sparse Hadamard matrix

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specific example

[0074] If you need to generate a sparse Hadamard matrix with a length of 16 and exactly 7 zeros in each row and column Specifically include:

[0075] 1. Apply the algorithm in step S103 to broken down into

[0076] Specifically, since 7=2 2 +2 1 +2 0 , that is, its binary sequence is expressed as (1, 1, 1), and it is easy to know that there are three 1s in its sequence, that is, Divide into 3 items. According to the method in step S103, the first step generates The second step is generated The third step is to generate

[0077] 2. Use steps S101 and S102 to generate

[0078] Specifically, first use the method of step S101 to generate

[0079] A 0 = 1 0 0 1 , B 0 ...

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Abstract

The invention discloses a compressed sensing observation matrix constructing method based on a sparse Hadamard matrix, which comprises the following steps of: A, establishing a first sparse Hadamard matrix set, wherein each first sparse Hadamard matrix in the first sparse Hadamard matrix set is shown in the specficiation; B, obtaining a second sparse Hadamard matrix set according to the first sparse Hadamard matrix set, wherein each second sparse Hadamard matrix in a second sparse Hadamard matrix set is shown in the specification; C, decomposing the sparse Hadamard matrixes to obtain matrixes with forms of the A and the B steps; D merging the matrixes with the forms of the A and the B steps to obtain the sparse Hadamard matrix; and E, extracting preset lines randomly to obtain the observation matrix. The observation matrix obtained through the compressed sensing observation matrix constructing method disclosed by the invention can reduce computation complexity of compressed sensing in compressed sampling and reconfiguration recovery of data. In addition, the observation matrix is more convenient for hardware realization.

Description

technical field [0001] The invention relates to the technical field of sparse signal processing, in particular to a method for constructing a compressed sensing observation matrix based on a sparse Hadamard matrix. Background technique [0002] In recent years, with the rapid development of digital signal processing, the amount of data to be processed is increasing at an alarming rate. The traditional Nyquist (Nyquist) sampling theorem requires that the sampling frequency of the signal is not less than twice the maximum frequency of the signal, which puts forward higher requirements for signal processing capabilities and hardware equipment. In order to break through the Nyquist sampling theory It is a traditional signal processing method for supporting information acquisition, compression processing, storage and transmission. A new compressed sensing theory that combines data acquisition and data compression into one has become one of the hotspots of research at home and ab...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03M7/30
Inventor 戴琼海李岩张永兵
Owner TSINGHUA UNIV
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