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Methods for converting partial Hadamard matrix to Gauss matrix

A Gaussian matrix and Hadar technology, which is applied in the field of transformation from partial Hadamard matrix to Gaussian matrix, can solve the problem of poor randomness of Hadamard matrix

Inactive Publication Date: 2014-07-23
程涛 +1
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

[0004] In order to solve the problem of poor randomness of partial Hadamard matrices and integrate the advantages of partial Hadamard matrices and Gaussian matrices, the present invention provides a conversion method from partial Hadamard matrices to Gaussian matrices

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  • Methods for converting partial Hadamard matrix to Gauss matrix
  • Methods for converting partial Hadamard matrix to Gauss matrix
  • Methods for converting partial Hadamard matrix to Gauss matrix

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specific Embodiment approach 1

[0015] Specific implementation mode one: according to the instructions attached figure 1 This embodiment will be specifically described. Partial Hadamard matrix to Gaussian matrix conversion method, the process of the method is:

[0016] Step 1: Generate Hadamard Matrix , left-multiplied random matrix and right multiplying the random matrix ,in , , , , and are all natural numbers;

[0017] Step two: Left multiply random matrix generate , right multiply random matrix generate ,make or or or , set the number of iterations i The initial value of 0, set the iteration error ;

[0018] Step 3: Calculation by Jarque-Bera test The number of rows that follow a Gaussian distribution for each column and row and number of columns ;calculate The correlation coefficient between each column vector, take the maximum value of its absolute value ;Calculate the correlation coefficient between each row vector, and take out the maximum value...

specific Embodiment approach 2

[0023] Specific implementation mode two: this specific implementation mode is a further description of the conversion method from the partial Hadamard matrix to the Gaussian matrix described in the specific implementation mode one, and the iterative error is set in step 2 err 1 for , err 2 for , err 3 for .

specific Embodiment approach 3

[0024] Specific embodiment three: This specific embodiment is a further description of the conversion method from the partial Hadamard matrix to the Gaussian matrix described in the specific embodiment one, and the orthogonal normalization described in step four Each row vector, and then the specific process of unitizing each column vector is: first Orthogonalize the row vectors, then normalize the row vectors, and finally normalize the column vectors.

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Abstract

The invention relates to methods for converting a partial Hadamard matrix to a Gauss matrix, belongs to the technical field of measurement matrix design and optimization in compressive sensing and provides three methods for partial Hadamard matrix to the Gauss matrix. The methods comprise the steps of first enabling the partial Hadamard matrix to undergo premultiplication or postmultiplication of a random matrix or performing no treatment on the partial Hadamard matrix, performing row vector orthogonal standardization and column vector unitization on a matrix worked out through (i-1)-iteration operation through i iterations, and finishing the conversion of the partial Hadamard matrix to the Gauss matrix with the maximums of correlated coefficient absolute values between row vectors and column vectors, the astringency of every row vector module and the numbers of rows and columns complying with gauss distribution as the criteria. The acquired Gauss matrix comprises two types which are a proximity matrix and an optimization matrix. According to the method, the obtained Gauss matrix simultaneously has the advantages of both partial Hadamard matrixes and the Gauss matrixes.

Description

technical field [0001] The invention belongs to the technical field of compressed sensing, and specifically provides a conversion method from a partial Hadamard matrix to a Gaussian matrix. Background technique [0002] Compressed sensing (Compressive sensing) can reconstruct the signal at a sampling rate far lower than the requirement of 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 detection...

Claims

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Application Information

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IPC IPC(8): H03M7/30G06F17/16
Inventor 程涛
Owner 程涛
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