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A high-dimensional sparse vector reconstruction method based on iqr_omp

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

Active Publication Date: 2021-06-01
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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  • A high-dimensional sparse vector reconstruction method based on iqr_omp
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  • A 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 the new residual recursive formu...

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Abstract

The invention discloses a high-dimensional sparse vector reconstruction method based on IQR_OMP. According to the characteristics of the least squares solution in each step of the OMP algorithm, an incremental IGR_OMP algorithm is proposed based on the Greville recursive process, and a series of useful recursive properties are obtained, which effectively improves the calculation speed; on the basis of the analysis of the IGR_OMP algorithm , using the relationship between Greville's recursive algorithm and QR decomposition, an incremental IQR_OMP algorithm based on QR decomposition is established, which effectively reduces the computational workload and improves the effectiveness of the algorithm in solving large-scale problems; high-dimensional sparse vector weight Simply speaking, the structure is to give the sparsest coefficient representation of high-dimensional vectors on the 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...

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Application Information

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Patent Type & Authority Patents(China)
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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