基于二進(jìn)制序列族的壓縮感知測量矩陣構(gòu)造

蘆存博; 肖嵩; 權(quán)磊

doi:10.11999/JEIT151076

基于二進(jìn)制序列族的壓縮感知測量矩陣構(gòu)造

doi: 10.11999/JEIT151076

基金項(xiàng)目:

國家自然科學(xué)基金(61372069)，高等學(xué)校學(xué)科創(chuàng)新引智計劃(111計劃)(B08038)

計量
- 文章訪問數(shù): 2018
- HTML全文瀏覽量: 191
- PDF下載量: 565
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2015-09-21
- 修回日期: 2016-01-20
- 刊出日期: 2016-07-19

Construction of Compressed Sensing Measurement Matrix Based on Binary Sequence Family

Funds:

The National Natural Science Foundation of China (61372069), The Programme of Introducing Talents of Discipline to Universities (111 Project) (B08038)

摘要

摘要: 構(gòu)造確定性測量矩陣對壓縮感知理論的推廣與應(yīng)用具有重要的意義。該文源于代數(shù)編碼理論，提出一種基于二進(jìn)制序列族的確定性測量矩陣構(gòu)造算法。相關(guān)性是描述矩陣性質(zhì)的重要準(zhǔn)則，減小相關(guān)性可使重建性能提高。該文推導(dǎo)出所構(gòu)造測量矩陣的相關(guān)性小于同條件下的高斯隨機(jī)矩陣和伯努利隨機(jī)矩陣。理論分析和仿真實(shí)驗(yàn)表明，該方式構(gòu)造的測量矩陣的重建性能優(yōu)于同條件下的高斯隨機(jī)矩陣和伯努利隨機(jī)矩陣；所構(gòu)造矩陣可由線性反饋移位寄存器結(jié)構(gòu)實(shí)現(xiàn)，易于硬件實(shí)現(xiàn)，有利于壓縮感知理論的實(shí)用化。
- 信號處理 /
- 壓縮感知 /
- 測量矩陣 /
- 二進(jìn)制序列族
Abstract: It is significant to construct deterministic measurement matrix for the promotion and application of the Compressed Sensing (CS) theory. Originating from the algebraic coding theory, a construction algorithm of Binary Sequence Family (BSF) based deterministic measurement matrix is presented. The coherence is an important criterion to describe the property of matrices. Lower coherence leads to higher reconstruction performance. The coherence of the proposed measurement matrix is derived to be smaller than the corresponding Gaussian random matrix and Bernoulli random matrix. Theoretical analysis and simulation results show that the proposed matrix can obtain better reconstruction results than the corresponding Gaussian random matrix and Bernoulli random matrix. The proposed matrix can make the hardware realization convenient and easy by means of Linear Feedback Shift Register (LFSR) structures, thus being conductive to practical compressed sensing.
- Signal processing /
- Compressed Sensing (CS) /
- Measurement matrix /
- Binary Sequence Family (BSF)

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參考文獻(xiàn)(21)

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