A Gaussian Matrix Optimization Method Based on Compressed Sensing

A Gaussian matrix and optimization method technology, applied in the field of compressed sensing and sparse signal processing, can solve the problem of low signal reconstruction ability of Gaussian matrix, and achieve the effect of improving signal reconstruction ability, wide application prospect, and preserving universality.

Active Publication Date: 2015-08-05
GUANGXI UNIVERSITY OF TECHNOLOGY
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  • Abstract
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  • Application Information

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Problems solved by technology

[0004] In order to solve the problem of low Gaussian matrix signal reconstruction ability, the present invention provides a Gaussian matrix optimization method

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  • A Gaussian Matrix Optimization Method Based on Compressed Sensing
  • A Gaussian Matrix Optimization Method Based on Compressed Sensing
  • A Gaussian Matrix Optimization Method Based on Compressed Sensing

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specific Embodiment approach 1

[0018] Specific implementation mode one: according to the instructions attached figure 1 This embodiment will be specifically described. The optimization process of a Gaussian matrix optimization method based on compressed sensing described in this embodiment is:

[0019] Step 1: Generate an independent and identically distributed Gaussian matrix Φ, where Φ∈R M×N , M-9 , err2 is 10 -9 , err3 is 10 -9 ;

[0020] Step 2: Use the Jarque-Bera test to calculate the number of rows J that do not obey the Gaussian distribution in each column and row of Φ ri and column number J ci ;

[0021] Step 3: Calculate the angle between each column vector of Φ, and take out its maximum value θ cimax and minimum θ cimin , and calculate the difference θ between the two i , calculate the angle between each row vector, and take out its maximum value θ rimax and minimum θ rimin ;

[0022] Step 4: Calculate the modulus of each row vector of Φ, and take out its maximum value norm rimax and...

specific Embodiment approach 2

[0029] Specific embodiment 2: This specific embodiment is a further description of a Gaussian matrix optimization method based on compressed sensing described in specific embodiment 1. In step 1, the iterative error err1 is set to 10 -9 , err2 is 10 -9 , err3 is 10 -9 .

specific Embodiment approach 3

[0030] Specific embodiment three: This specific embodiment is a further description of a Gaussian matrix optimization method based on compressed sensing described in specific embodiment one, the orthogonal normalization of each row vector of Φ described in step five, and the unitization of each column vector of Φ The specific process of is as follows: firstly, each row vector of Φ is orthogonalized, then each row vector is normalized, and finally each column vector is normalized.

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Abstract

A compressive sensing based Gaussian matrix optimizing method belongs to the technical field of measuring matrix optimization in compressive sensing and solves the problem of poor signal reconstruction capability of Gaussian matrix measuring matrix. The compressive sensing based Gaussian matrix optimizing method includes: subjecting row vectors to orthogonal standardization and column vectors to unitization for measuring matrix computed by the (i-1)th iteration through the ith iteration and completing optimization of Gaussian matrix by utilizing range of included angles among the column vectors, the maximum value and the minimum value of the included angles among the row vectors, the maximum value and the minimum value of row vector modules and the number of rows and columns inadaptive to Gaussian distribution as reference. The compressive sensing based Gaussian matrix optimizing method is applicable to optimization of Gaussian measuring matrix in the compressive sensing.

Description

technical field [0001] The invention belongs to the technical field of compressed sensing and sparse signal processing, and specifically provides an optimization and construction method of a Gaussian matrix. Background technique [0002] Compressed sensing (Compressive sensing) can reconstruct the signal at a sampling rate far lower than that required by the Nyquist sampling theorem; it realizes the simplification of the data encoding end (acquisition, compression, encryption, transmission) and the decoding end (decompression, Refactoring) complex data processing landscape. Data compression and encryption are realized during the data acquisition process, and high-dimensional signals are directly converted into low-dimensional signals. Compressed sensing has broad application prospects in image processing, video analysis, radar remote sensing, communication coding, data mining and other fields, and will generate huge economic benefits in military reconnaissance, resource det...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/16
Inventor 程涛
Owner GUANGXI UNIVERSITY OF TECHNOLOGY
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