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IGR_OMP based high-dimension sparse vector reconstruction method

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: 2018-09-25
NANJING UNIV
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Problems solved by technology

Although the classic OMP (Orthogonal Matching Pursuit, Orthogonal Matching Pursuit) algorithm is less complex than other non-greedy algorithms, it still has a distance from real-time signal processing in practical applications.

Method used

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  • IGR_OMP based high-dimension sparse vector reconstruction method
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  • IGR_OMP based high-dimension sparse vector reconstruction method

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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 an IGR_OMP based high-dimension sparse vector reconstruction method. An incremental IGR_OMP algorithm is provided according the characteristic that the least square solution needs to be calculated in each step of an OMP algorithm and on the basis of a Greville recursion process, a series of useful recursion properties is obtained, and the calculation speed is improved effectively. On the basis of analysis on the IGR_OMP algorithm, relation between the Greville recursion algorithm and QR decomposition is used, the incremental IQR_OMP algorithm on the basis of QR decomposition is established, the workload of calculation is reduced effectively, The algorithm can be used to solve a large problem more effectively; and simply, high-dimension sparse vector reconstruction provides a sparsest coefficient representation of the high-dimension vector in a complete vector system.

Description

technical field [0001] The invention relates to an IGR_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...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06K9/46G06F17/16
CPCG06F17/16G06V10/40G06V10/513
Inventor 赵健申富饶董珍君赵金煕
Owner NANJING UNIV
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