本文選題：壓縮感知 + 重構(gòu)算法��； 參考：《西安電子科技大學(xué)》2014年碩士論文

【摘要】：全新的信號(hào)處理理論-壓縮感知理論是根據(jù)信號(hào)的稀疏特性或可壓縮性質(zhì)提出來的。它打破了限定采樣速率的Nyquist采樣定理,摒棄了先進(jìn)行采樣再實(shí)施壓縮的信號(hào)處理模式,使得信號(hào)采樣過程與壓縮過程同時(shí)進(jìn)行。通過求解優(yōu)化問題就可以重構(gòu)信號(hào),從而有效的避免了大量采樣數(shù)據(jù)的需求,同時(shí)解決了采樣所得數(shù)據(jù)的存儲(chǔ)、傳輸?shù)雀叱杀締栴},為實(shí)現(xiàn)高效的信號(hào)處理帶來了巨大的進(jìn)展。該理論包含三個(gè)基本內(nèi)容:稀疏表示信號(hào)、選取觀測矩陣以及構(gòu)造重構(gòu)算法。其中所選算法的效果及收斂速度直接決定著該理論是否切實(shí)可行。因此壓縮感知理論的核心內(nèi)容是設(shè)計(jì)高效的重構(gòu)算法。本文是在對(duì)壓縮感知理論的基本知識(shí)及現(xiàn)有重構(gòu)算法系統(tǒng)學(xué)習(xí)的前提下,研究了以下幾方面的內(nèi)容:首先,簡要闡述了研究壓縮感知的背景及意義,目前的研究現(xiàn)狀以及典型的應(yīng)用領(lǐng)域,并詳細(xì)介紹了壓縮感知理論的基礎(chǔ)知識(shí)。其次,在各種重構(gòu)算法中,深入研究了幾種常用的凸松弛算法,同時(shí)研究了幾種新穎的非單調(diào)線搜索方法,并在此基礎(chǔ)上給出了一個(gè)改進(jìn)的非單調(diào)線搜索Barzilai-Borwein梯度法。通過大量的仿真實(shí)驗(yàn),發(fā)現(xiàn)在達(dá)到相同的相對(duì)誤差時(shí),改進(jìn)的信號(hào)重構(gòu)算法需要較少的迭代次數(shù),但是其運(yùn)行時(shí)間卻比非單調(diào)Barzilai-Borwein梯度法有所增加。最后,針對(duì)上述算法存在的問題,提出了新非單調(diào)線搜索Barzilai-Borwein梯度算法。該算法在充分利用新非單調(diào)線搜索方法的收斂特性的基礎(chǔ)上,通過目標(biāo)函數(shù)的近似函數(shù)來搜尋最優(yōu)解,從而獲得迭代方向的取值,再利用新非單調(diào)線搜索方法求得步長。仿真結(jié)果表明,新非單調(diào)線搜索Barzilai-Borwein梯度算法不僅可以降低算法的運(yùn)行時(shí)間,而且明顯減少了算法的迭代次數(shù),從而使得算法的收斂速度大大提高,算法的重構(gòu)性能大大增強(qiáng)。
[Abstract]:A new signal processing theory, compression sensing theory, is proposed based on the sparse or compressible properties of signals. It breaks the Nyquist sampling theorem which limits the sampling rate and abandons the signal processing mode of sampling first and then compressing so that the signal sampling process and the compression process are carried out simultaneously. By solving the optimization problem, we can reconstruct the signal, thus effectively avoid the need of a large number of sampled data, at the same time, solve the problem of storage and transmission of the sampled data, and bring great progress for the realization of efficient signal processing. The theory includes three basic contents: sparse representation signal, selection of observation matrix and reconstruction algorithm. The effect and convergence speed of the selected algorithm directly determine the feasibility of the theory. Therefore, the core of compressed perception theory is to design efficient reconstruction algorithm. Based on the basic knowledge of compression perception theory and the learning of existing reconstruction algorithms, this paper studies the following aspects: firstly, the background and significance of the research on compression perception are briefly described. The present research situation and typical application field are introduced, and the basic knowledge of compressed perception theory is introduced in detail. Secondly, among all kinds of reconstruction algorithms, several commonly used convex relaxation algorithms are deeply studied, and several novel non-monotone line search methods are studied, and an improved non-monotone line search Barzilai-Borwein gradient method is presented. Through a large number of simulation experiments, it is found that the improved signal reconstruction algorithm needs less iterations when the relative error is the same, but its running time is longer than that of the non-monotone Barzilai-Borwein gradient method. Finally, a new nonmonotone line search Barzilai-Borwein gradient algorithm is proposed to solve the problem. On the basis of making full use of the convergence of the new nonmonotone line search method, the algorithm searches for the optimal solution by the approximate function of the objective function, and then obtains the value of the iteration direction, and then uses the new nonmonotone line search method to obtain the step size. Simulation results show that the new non-monotone line search Barzilai-Borwein gradient algorithm can not only reduce the running time of the algorithm, but also obviously reduce the number of iterations of the algorithm, so that the convergence speed of the algorithm is greatly improved, and the reconstruction performance of the algorithm is greatly enhanced.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.7

【相似文獻(xiàn)】

相關(guān)期刊論文 前10條

1 劉盾;石和平;;基于一種改進(jìn)的壓縮感知重構(gòu)算法的分析與比較[J];科學(xué)技術(shù)與工程;2012年21期

2 蔣英春;;離散空間中正交小波分解重構(gòu)算法的實(shí)現(xiàn)[J];計(jì)算機(jī)應(yīng)用研究;2013年02期

3 劉勇;魏東紅;毛京麗;;基于優(yōu)化內(nèi)積模型的壓縮感知快速重構(gòu)算法[J];北京郵電大學(xué)學(xué)報(bào);2013年01期

4 王田川;宋建新;;壓縮感知重構(gòu)算法研究[J];電視技術(shù);2013年11期

5 李福建,陳廷槐,田梅,周六丁;一種新的環(huán)網(wǎng)故障診斷與重構(gòu)算法[J];計(jì)算機(jī)工程;1992年06期

6 童露霞;王嘉;;基于壓縮傳感的重構(gòu)算法研究[J];電視技術(shù);2012年11期

7 李博;郭樹旭;;一種改進(jìn)的壓縮感知重構(gòu)算法研究[J];現(xiàn)代電子技術(shù);2013年03期

8 李志剛;;一種快速的壓縮感知信號(hào)重構(gòu)算法[J];信息技術(shù);2013年06期

9 梁棟,楊尚俊,章權(quán)兵;一種基于圖象序列的3D重構(gòu)算法[J];安徽大學(xué)學(xué)報(bào)(自然科學(xué)版);2001年01期

10 陳勤;鄒志兵;張e，

本文編號(hào)：1961018