一種用于壓縮感知理論的投影矩陣優(yōu)化算法

吳光文; 張愛(ài)軍; 王昌明

doi:10.11999/JEIT141450

一種用于壓縮感知理論的投影矩陣優(yōu)化算法

doi: 10.11999/JEIT141450

2.
(南京理工大學(xué)機(jī)械工程學(xué)院南京 210094) ②(東華理工大學(xué)電子與機(jī)械工程學(xué)院撫州 344000)

基金項(xiàng)目:

國(guó)家自然科學(xué)基金(61161010, 11265001)和高等學(xué)校博士學(xué)科點(diǎn)專(zhuān)項(xiàng)科研基金(20133219110027)

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- 文章訪(fǎng)問(wèn)數(shù): 1562
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- 被引次數(shù): 0
出版歷程
- 收稿日期: 2014-11-20
- 修回日期: 2015-02-11
- 刊出日期: 2015-07-19

Novel Optimization Method for ProjectionMatrix in Compress Sensing Theory

2.
(School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China)

摘要

摘要: 考慮到投影矩陣對(duì)壓縮感知(CS)算法性能的影響，該文提出一種優(yōu)化投影矩陣的算法。該方法提出可導(dǎo)的閾值函數(shù)，通過(guò)收縮Gram矩陣非對(duì)角元的方法壓縮投影矩陣和稀疏字典的相關(guān)系數(shù)，引入基于沃爾夫條件(Wolfes conditions)的梯度下降法求解最佳投影矩陣，達(dá)到提高投影矩陣優(yōu)化算法穩(wěn)定度和重構(gòu)信號(hào)精度的目的。通過(guò)基追蹤(BP)算法和正交匹配追蹤(OMP)算法求解l0優(yōu)化問(wèn)題，用壓縮感知方法實(shí)現(xiàn)隨機(jī)稀疏向量、小波測(cè)試信號(hào)和圖像信號(hào)的感知和重構(gòu)。仿真實(shí)驗(yàn)表明，該文提出的投影矩陣優(yōu)化算法能較大地提高重構(gòu)信號(hào)的精度。
- 壓縮感知 /
- 相干性 /
- 基追蹤算法 /
- 正交匹配追蹤算法
Abstract: Considering the influence of the projection matrix on Compressed Censing (CS), a novel method is proposed to optimize the projection matrix. In order to improve the signals reconstruction precise and the stability of the optimization algorithm of the projection matrix, the proposed method adopts a differentiable threshold function to shrink the off-diagonal items of a Gram matrix corresponding to the mutual coherence between the projection matrix and sparse dictionary, and introduces a gradient descent approach based on the Wolfs-conditions to solve the optimization projection matrix. The Basis-Pursuit (BP) algorithm and the Orthogonal Matching Pursuit (OMP) algorithm are applied to find the solution of the minimuml0-norm optimization issue and the compressed sensing are utilized to sense and reconstruct the random vectors, wavelets noise test signals and pictures. The results of the simulation show the proposed method based on the projection matrix optimization is able to improve the quality of the reconstruction performance.
- Compressed Sensing (CS) /
- Mutual coherence /
- Basis-Pursuit (BP) algorithm /
- Orthogonal Matching- Pursuit (OMP) algorithm

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參考文獻(xiàn)(19)

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