本文關(guān)鍵詞：基于相位恢復(fù)閾值算法與內(nèi)投影神經(jīng)網(wǎng)絡(luò)算法的稀疏信號(hào)重構(gòu)　出處：《西南大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 壓縮感知 稀疏信號(hào)恢復(fù) 相位恢復(fù) 硬閾值 神經(jīng)網(wǎng)絡(luò)算法

【摘要】：隨著信息技術(shù)的發(fā)展和大數(shù)據(jù)時(shí)代的到來(lái),人們對(duì)信息量的需求也在不斷地增加,這給信號(hào)數(shù)據(jù)的采樣、存儲(chǔ)和傳輸帶來(lái)了新的挑戰(zhàn).稀疏信號(hào)恢復(fù)問(wèn)題越來(lái)越受到關(guān)注,并且在信號(hào)處理、壓縮感知、機(jī)器學(xué)習(xí)、統(tǒng)計(jì)學(xué)等領(lǐng)域應(yīng)用廣泛.本文以壓縮感知為基礎(chǔ),選取特殊的測(cè)量矩陣,對(duì)稀疏信號(hào)數(shù)據(jù)的重構(gòu)進(jìn)行了研究.本文主要內(nèi)容如下:第一章簡(jiǎn)述了壓縮感知和稀疏信號(hào)恢復(fù)的研究背景,概述了國(guó)內(nèi)外對(duì)壓縮感知和稀疏信號(hào)恢復(fù)的研究歷史及研究現(xiàn)狀,總結(jié)了本文的主要工作和全文的組織結(jié)構(gòu).第二章闡述了稀疏信號(hào)數(shù)據(jù)的重構(gòu)理論,主要包括三大核心問(wèn)題,即信號(hào)的稀疏表示、測(cè)量矩陣設(shè)計(jì)和信號(hào)的重構(gòu)算法設(shè)計(jì).第三章介紹了稀疏信號(hào)的相位恢復(fù)問(wèn)題,研究了在相位信息缺乏的情況下的稀疏信號(hào)恢復(fù),提出了一種用新的迭代硬閾值(IHT)算法來(lái)解決相位恢復(fù)問(wèn)題.接下來(lái)在IHT算法中加入回溯的思想,即基于回溯的迭代硬閾值算法(BIHT),克服了IHT不穩(wěn)定的缺點(diǎn),并且提高了計(jì)算的速度和精度.第四章提出了稀疏信號(hào)重構(gòu)問(wèn)題的的內(nèi)點(diǎn)投影神經(jīng)網(wǎng)絡(luò)(IPNN)算法.首先介紹了一個(gè)非凸的極小化問(wèn)題,提出了利用高相干性的測(cè)量矩陣進(jìn)行稀疏信號(hào)重構(gòu).通過(guò)引入IPNN解決非凸的極小化問(wèn)題,并在一定的條件下,證明了IPNN的收斂性.最后,通過(guò)一系列的實(shí)驗(yàn)表明了IPNN對(duì)于極小化方法的有效性.第五章歸納總結(jié)了全文所做的工作,并對(duì)本文可以繼續(xù)研究的內(nèi)容作了分析與展望.
[Abstract]:With the development of information technology and the arrival of big data, the demand for information is also increasing, the data acquisition, storage and transmission has brought new challenges. The sparse signal recovery problem more and more attention, and in signal processing, compressed sensing, machine learning, statistics and other fields of application widely. Based on the compressed sensing measurement matrix, selection of special data, the reconstruction of sparse signals is studied. The main contents of this paper are as follows: the first chapter introduces the research background of compressed sensing and sparse signal recovery, both at home and abroad are summarized on compressed sensing and sparse signal recovery the research history and present research, summary the organization structure and the main work of this paper. The second chapter expounds the theory of sparse signal reconstruction data, including the three core issues, namely signal sparse representation, measurement matrix The design of array design and signal reconstruction algorithm. The third chapter introduces the phase retrieval problem of sparse signal, sparse signal phase information in the absence of recovery, and presents a new iterative hard thresholding (IHT) algorithm to solve the problem of phase retrieval. Then add the idea back in the IHT algorithm. Based on the iterative hard thresholding of backtracking algorithm (BIHT), IHT overcomes the shortcomings of instability and improve the speed and accuracy of calculation. The fourth chapter puts forward the projection neural network point sparse signal reconstruction problem in (IPNN) algorithm. First introduced a non convex minimization problem, put forward sparse signal reconstruction using the measurement matrix with high coherence. To solve non convex minimization problem by introducing IPNN, and under certain conditions, convergence of the IPNN. Finally, through a series of experiments show that the IPNN for the minimum The fifth chapter summarizes the work done in the full text, and makes an analysis and Prospect of the content that can continue to be studied in this article.

【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TP183;TN911.7

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