High-dimensional sparse vector reconstruction method based on IQR_OMP

A technology of sparse vectors and vectors, applied in the field of high-dimensional sparse vector reconstruction, which can solve problems such as low complexity

Active Publication Date: 2018-10-16
NANJING UNIV
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Problems solved by technology

Although the classic OMP (Orthogonal Matching Pursuit, Orthogonal Matching Pursuit) algorithm is less complex ...

Method used

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  • High-dimensional sparse vector reconstruction method based on IQR_OMP
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Embodiment

[0200] The computing environment for designing numerical experiments in this paper is DELL-PC WORK GROUP Intel(R) Core(TM) i7-4790 3.6Ghz, memory 8.0GB, Windows 7 Ultimate Edition, and the computing software is MATLAB R2010b.

[0201] A∈R in Case1 2000×5000 , K=600;

[0202] A∈R in Case2 3000×6000 , K=1000;

[0203] A∈R in Case3 10000×15000 , K=3000;

[0204] The calculation time comparison of the incremental OMP algorithm 1-D is shown in Table 1 below:

[0205] Table 1

[0206] type of situation

IQR_OMP

IGR_OMP

OMP

Case1

7.6331

9.112

30.8978

Case2

29.2647

34.8170

164.7083

Case3

810.4921

962.1627

10386.0

[0207] The above three algorithms are described as follows:

[0208] 1. The IQR_OMP algorithm is an algorithm based on QR decomposition and a new residual recursive formula given in this paper;

[0209] 2. The IGR_OMP algorithm is the OMP algorithm based on the Greville recursive formula and th...

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Abstract

The invention discloses a high-dimensional sparse vector reconstruction method based on IQR_OMP. According to the characteristic of the OMP algorithm in which calculate the least square solution in each step, an incremental IGR_OMP algorithm is proposed based on the Greville recursive process, and a series of useful recursive properties are obtained, so that the calculation speed is effectively improved. The incremental IQR _ OMP algorithm on the basis of QR decomposition is established, based on analyzing the IGR _ OMP algorithm, by utilizing the relationship between the Greville recursive algorithm and the QR decomposition, so that the calculation workload is effectively reduced, and the effectiveness of the algorithm to solve large problems is improved. In addition, the high-dimensionalsparse vector reconstruction is simply to give the most sparse coefficient representation of a high-dimensional vector on an over-complete vector system.

Description

technical field [0001] The invention relates to an IQR_OMP-based high-dimensional sparse vector reconstruction method. Background technique [0002] Compressive Sensing (CS for short) is a new key technology in the field of image or signal processing. Its essence is to use information far below the dimension of signal vector or image vector to effectively determine the sparsest coefficient representation of this high-dimensional vector on an over-complete dictionary. The core problem is to solve a sparse solution of a subdefinite linear system. To reconstruct the signal or image vector (Reference: Yan Jingwen et al., Compressed Sensing and Application, 2015, National Defense Industry Press, Beijing. E.J.Candès, M.Wakin, "people hearing without listening" An introduction to compressive sampling, IEEE Signal Processing Magazine, 2008, 25(2), 21-30.). [0003] High-dimensional sparse vector reconstruction is a very important problem in the field of signal processing and image...

Claims

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Application Information

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IPC IPC(8): G06F17/16
CPCG06F17/16
Inventor 赵健申富饶董珍君赵金煕
Owner NANJING UNIV
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