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Compressed sensing system and dimensionality reduction method of signal formula of compressed sensing system

A technology of compressed sensing and signals, applied in the field of image processing, can solve problems such as the inability to completely solve the problem of determining the RIP nature of the measurement matrix

Inactive Publication Date: 2017-06-20
安凯
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Problems solved by technology

It can be seen that the irrelevance theory cannot completely solve the problem of judging whether the measurement matrix has the property of RIP, it is just a helpless move when the RIP criterion is difficult to judge whether a matrix can be used as a compressed sensing measurement matrix

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  • Compressed sensing system and dimensionality reduction method of signal formula of compressed sensing system
  • Compressed sensing system and dimensionality reduction method of signal formula of compressed sensing system
  • Compressed sensing system and dimensionality reduction method of signal formula of compressed sensing system

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Embodiment Construction

[0012] If an N-dimensional real-space digital signal X is compressible under some N N-dimensional orthogonal basis Ψ, then X can be expressed as X=ΨS, where S is a k-sparse vector. Use m to represent the minimum value of all non-zero components of these k-sparse vectors, record c=min(0, m), and for i=1, 2,..., N, when s i ≠0 season And record The "T" in the upper right corner means transpose, then S * is a k-sparse vector with all nonzero components greater than zero.

[0013] Construct a M×N (M* Observations are made, and the measurement vector obtained is denoted as

[0014] y=ΦS *

[0015] where y is an M×1 vector. To make the equation y=ΦS * For any N-dimensional k-sparse vector S * To have a definite solution, any k column vectors of Φ must be linearly independent. According to the relevant knowledge of probability theory, when the components of the column vector of Φ are independent and identically distributed continuous random variables, the probability of an...

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Abstract

A dimensionality reduction method for a compressed sensing system and its signal equation is disclosed. After representing the original signal as the product of an orthogonal matrix and a sparse vector, the system output is the product of the measurement matrix and a sparse column vector. In order to recover sparse vectors from such signal equations, a dimensionality reduction method for signal equations is given, that is, removing most of the column components corresponding to the zero components of the sparse vectors in the measurement matrix. All the column vectors corresponding to the non-zero components of the sparse vector and the non-zero components of the sparse vector can be obtained by using the exhaustive method in the remaining column vectors. The product of the obtained sparse vector and the orthogonal matrix is ​​the original signal.

Description

technical field [0001] The invention relates to an image processing method. Background technique [0002] Compressed sensing theory, which has gradually emerged since 2006, provides new signal sampling and reconstruction methods, which break through the limit of the traditional Nyquist sampling theorem, and greatly reduce the number of sampling while obtaining high signal recovery quality. An imaging system and an attractive theory of information acquisition. Compressed sensing achieves compression while sampling. [0003] If the N-dimensional real-space digital signal X is compressible under certain N N-dimensional orthogonal bases, then X can be expressed as X=ΨS, where S is an N-dimensional vector with no more than k (<<M) non-zero components , called k-sparse vector, Ψ is an N×N matrix composed of N N-dimensional orthogonal basis. Design a stable M×N (M<N) measurement matrix Φ that is uncorrelated with the transformation basis Ψ to observe the signal X, and o...

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Application Information

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IPC IPC(8): H03M7/30
CPCH03M7/3062
Inventor 安培亮王晓英安宏亮
Owner 安凯
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