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Sensing matrix construction method based on Bernoulli shifting chaos sequence

A chaotic sequence and perceptual matrix technology, applied in electrical components, code conversion, analog-to-digital converters, etc., can solve problems such as large storage space and unsatisfactory RIP

Inactive Publication Date: 2014-07-16
SICHUAN UNIV
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  • Application Information

AI Technical Summary

Problems solved by technology

[0012] In order to overcome the large storage space required by the random sensing matrix, and the defects of not satisfying RIP in some cases, the present invention proposes a construction method of a pseudo-random sensing matrix based on n-way Bernoulli shift chaotic sequences

Method used

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  • Sensing matrix construction method based on Bernoulli shifting chaos sequence
  • Sensing matrix construction method based on Bernoulli shifting chaos sequence
  • Sensing matrix construction method based on Bernoulli shifting chaos sequence

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Embodiment Construction

[0035] The present invention will be further described below in conjunction with the accompanying drawings.

[0036] According to the description of specific steps in the summary of the invention, the structure of the perception matrix BCSM is as follows:

[0037] 1. First, select the parameter x1=0.45467 to construct the sequence

[0038]

[0039] .

[0040] 2, pair the sequence with the parameter l=5 Sampling to get the sequence .

[0041] Here, the sequence obtained by sampling with the parameter l=5 can satisfy the independent and identical distribution characteristics.

[0042] 3. Column-by-column construction The perception matrix BCSM:

[0043] .

[0044] The initial signal used in the experiment is a discrete-time sparse signal x with length n=200 s1 , with the distribution It is formed by independently extracting k points and assigning non-zero values, that is, the sparse matrix of the signal is the identity matrix I. In the simulation, Gaussi...

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Abstract

The invention discloses a sensing matrix construction method based on a Bernoulli shifting chaos sequence (BCSM). A matrix can meet an RIP in a high-probability mode and is then applied to data safety communication. N-path Bernoulli shifting mapping is a determinacy system and is a segmented linear chaotic mapping, therefore the chaos sequence can be very easy to reconstruct only by controlling a parameter n and an initial condition x1, and the reconstruction is easy to achieve in hardware and software. Due to the fact that the BCSM is a determinacy matrix including determinacy elements, the BCSM needs a smaller storage space compared with the random matrix, in addition, the BCSM is generally an approximate independent and identically distributed matrix, and therefore the BCSM is unrelated to sparse domain Psi selection and meets the RIP in the high-probability mode. The sensing matrix construction method has the advantage that the sensing matrix construction method is particularly prominent in application of signal xs sparse degree self-adaptation changes along with time.

Description

technical field [0001] The invention relates to a method for constructing a perception matrix in a compressed sensing theory. Background technique [0002] Traditional signal processing is based on the Nyquist sampling theorem. In order to accurately restore the original data, it is necessary to sample at a rate greater than or equal to twice the signal bandwidth, which increases the requirements for the hardware acquisition system. On the other hand, in practical applications, in order to reduce the amount of data stored, processed and transmitted, the sampled data is usually compressed. This creates a problem. Since the sampled data needs to be compressed, is it possible to discard useless information during the data collection process and only collect useful information? This is the compressed sensing theory developed in recent years. [0003] Compressed sensing (CS) is a sampling theory proposed by Cand`es and Tao. Under the condition of sparse or compressible signals,...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03M1/12H03M7/30
Inventor 李智干红平邓伯华
Owner SICHUAN UNIV
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