壓縮感知恢復(fù)算法及應(yīng)用研究
發(fā)布時(shí)間：2018-08-26 18:58
【摘要】：基于信號(hào)的稀疏性結(jié)構(gòu)，集采樣和壓縮為一體，壓縮感知突破了香農(nóng)采樣定理，能夠運(yùn)用遠(yuǎn)少于香農(nóng)采樣定理所界定的采樣數(shù)目來(lái)精確恢復(fù)原始稀疏信號(hào)。壓縮感知具有廣泛的應(yīng)用背景，包括誤差校正、圖像處理、通信工程、盲信號(hào)分離、模式識(shí)別等。壓縮感知的研究，促進(jìn)了信號(hào)處理理論和工程應(yīng)用的發(fā)展，已經(jīng)成為該領(lǐng)域的研究熱點(diǎn)之一。 信號(hào)恢復(fù)算法是壓縮感知理論的重要組成部分。針對(duì)不同的稀疏信號(hào)，選擇合適的恢復(fù)算法，運(yùn)用盡可能少的測(cè)量數(shù)目，壓縮感知致力于精確恢復(fù)原稀疏信號(hào)。本文以此為目標(biāo)，針對(duì)恢復(fù)算法展開(kāi)研究，主要貢獻(xiàn)如下： 1.基于硬閾值追蹤算法（hard thresholding pursuit，HTP），提出了一種新的貪婪算法，旨在解決信號(hào)稀疏度未知情況下的恢復(fù)性問(wèn)題。該算法采用了漸近估計(jì)稀疏度的技巧，解決真實(shí)稀疏度未知造成的困難。將限制等距性質(zhì)（restricted isometryproperty，RIP）作為理論分析工具，給出了算法收斂的充分條件，并且給出了恢復(fù)的信號(hào)與原始信號(hào)之間的誤差上界。在信號(hào)稀疏度未知的前提下，合成信號(hào)和自然圖像的恢復(fù)實(shí)驗(yàn)表明該算法具有良好的恢復(fù)性能。 2.目前，針對(duì)塊正交匹配追蹤算法（block orthogonal matching pursuit，BOMP）精確恢復(fù)原始?jí)K稀疏信號(hào)的條件大多以塊-互相關(guān)度（block mutual coherence）為判別準(zhǔn)則。利用塊-RIP，本文給出了保證BOMP算法精確恢復(fù)原信號(hào)的充分條件，并且說(shuō)明了給出基于塊-RIP的精確恢復(fù)條件是必要的；針對(duì)人臉識(shí)別等工程應(yīng)用中可能出現(xiàn)冗余塊的情況，提出了一種解決冗余塊問(wèn)題的算法，并且給出了保證算法精確恢復(fù)的條件；在多重測(cè)量向量（multiple measurement vectors，MMV）模型的基礎(chǔ)上，本文所提的算法能夠?qū)崿F(xiàn)同時(shí)處理多個(gè)樣本。最后，通過(guò)人臉識(shí)別的實(shí)驗(yàn)，表明了所提算法的有效性。 3.針對(duì)所求稀疏信號(hào)部分支撐信息已知的情況，提出了加權(quán)L2,1最小化方法。該方法可以利用信號(hào)序列中幀與幀之間的相關(guān)性，，將上一幀的支撐信息作為恢復(fù)下一幀信號(hào)的先驗(yàn)信息，使得進(jìn)一步降低采樣數(shù)目成為可能。利用RIP，給出了恢復(fù)的信號(hào)與原始信號(hào)之間的誤差上界。另外，由于該方法將二維的信號(hào)直接看做矩陣來(lái)處理，而不是將其向量化，這樣大大的減少了運(yùn)行時(shí)間。通過(guò)恢復(fù)Larynx圖像序列的實(shí)驗(yàn)，驗(yàn)證了算法的有效性。 4.針對(duì)貪婪塊坐標(biāo)下降算法（greedy block coordinate descent，GBCD），在加性噪聲和乘性噪聲干擾下，運(yùn)用RIP理論工具，分析了該算法的性能。給出了保證GBCD算法精確恢復(fù)原始信號(hào)的支撐集合的充分條件，并且給出了滿足該充分條件的例子；討論了該充分條件的上界，通過(guò)例子，指出了在不滿足該充分條件時(shí)，存在著GBCD算法不能精確恢復(fù)的情況。最后，通過(guò)仿真實(shí)驗(yàn)，驗(yàn)證了GBCD算法的性能。
[Abstract]:Based on the sparse structure of signal, which integrates sampling and compression, the compression perception breaks through the Shannon sampling theorem, and it can accurately restore the original sparse signal by using the number of samples defined by Shannon sampling theorem, which is far less than the number of samples defined by Shannon sampling theorem. Compression sensing has a wide range of applications, including error correction, image processing, communication engineering, blind signal separation, pattern recognition and so on. The research of compression sensing, which promotes the development of signal processing theory and engineering application, has become one of the research hotspots in this field. Signal recovery algorithm is an important part of compression perception theory. For different sparse signals, the appropriate restoration algorithm is selected, and the number of measurements is as small as possible. The compression sensing is devoted to the accurate restoration of the original sparse signals. In this paper, the main contributions of this paper are as follows: 1. Based on the hard threshold tracking algorithm (hard thresholding pursuit,HTP), a new greedy algorithm is proposed to solve the recovery problem with unknown signal sparsity. The algorithm uses the technique of asymptotic estimation of sparsity to solve the difficulty caused by unknown real sparsity. Using the restricted equidistant property (restricted isometryproperty,RIP) as a theoretical analysis tool, the sufficient conditions for the convergence of the algorithm are given, and the upper bound of the error between the recovered signal and the original signal is given. Under the condition that the signal sparsity is unknown, the experimental results of synthetic signal and natural image show that the algorithm has good recovery performance. 2. At present, for block orthogonal matching tracking algorithm (block orthogonal matching pursuit,BOMP), most of the conditions for accurate restoration of original block sparse signals are based on block-mutual correlation degree (block mutual coherence) criteria. By using block -RIPs, this paper gives sufficient conditions to guarantee the accurate restoration of original signals by BOMP algorithm, and explains the necessity of giving accurate restoration conditions based on block -RIP, aiming at the possible occurrence of redundant blocks in engineering applications such as face recognition. This paper proposes an algorithm to solve the redundant block problem, and gives the conditions to ensure the accurate recovery of the algorithm. On the basis of the multi-measurement vector (multiple measurement vectors,MMV) model, the algorithm proposed in this paper can process multiple samples at the same time. Finally, the experiments of face recognition show that the proposed algorithm is effective. In this paper, a weighted L _ 2N _ 1 minimization method is proposed to minimize the partial support information of the sparse signal. This method can take advantage of the correlation between frame and frame in the signal sequence and use the support information of the previous frame as the prior information of the signal of the next frame, which makes it possible to further reduce the number of samples. The error upper bound between the recovered signal and the original signal is given by using RIP,. In addition, because the two-dimensional signal is treated as matrix instead of vectorization, the running time is greatly reduced. The effectiveness of the algorithm is verified by the experiment of restoring Larynx image sequence. 4. 4. Aiming at the greedy block coordinate descent algorithm (greedy block coordinate descent,GBCD), the performance of the algorithm is analyzed by using RIP theory under additive noise and multiplicative noise interference. A sufficient condition is given to guarantee the accurate restoration of the support set of the original signal by the GBCD algorithm, and an example of satisfying the sufficient condition is given, the upper bound of the sufficient condition is discussed, and it is pointed out that if the sufficient condition is not satisfied, There exists the situation that the GBCD algorithm can not recover accurately. Finally, the performance of GBCD algorithm is verified by simulation experiments.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.7
本文編號(hào)：2205849
[Abstract]:Based on the sparse structure of signal, which integrates sampling and compression, the compression perception breaks through the Shannon sampling theorem, and it can accurately restore the original sparse signal by using the number of samples defined by Shannon sampling theorem, which is far less than the number of samples defined by Shannon sampling theorem. Compression sensing has a wide range of applications, including error correction, image processing, communication engineering, blind signal separation, pattern recognition and so on. The research of compression sensing, which promotes the development of signal processing theory and engineering application, has become one of the research hotspots in this field. Signal recovery algorithm is an important part of compression perception theory. For different sparse signals, the appropriate restoration algorithm is selected, and the number of measurements is as small as possible. The compression sensing is devoted to the accurate restoration of the original sparse signals. In this paper, the main contributions of this paper are as follows: 1. Based on the hard threshold tracking algorithm (hard thresholding pursuit,HTP), a new greedy algorithm is proposed to solve the recovery problem with unknown signal sparsity. The algorithm uses the technique of asymptotic estimation of sparsity to solve the difficulty caused by unknown real sparsity. Using the restricted equidistant property (restricted isometryproperty,RIP) as a theoretical analysis tool, the sufficient conditions for the convergence of the algorithm are given, and the upper bound of the error between the recovered signal and the original signal is given. Under the condition that the signal sparsity is unknown, the experimental results of synthetic signal and natural image show that the algorithm has good recovery performance. 2. At present, for block orthogonal matching tracking algorithm (block orthogonal matching pursuit,BOMP), most of the conditions for accurate restoration of original block sparse signals are based on block-mutual correlation degree (block mutual coherence) criteria. By using block -RIPs, this paper gives sufficient conditions to guarantee the accurate restoration of original signals by BOMP algorithm, and explains the necessity of giving accurate restoration conditions based on block -RIP, aiming at the possible occurrence of redundant blocks in engineering applications such as face recognition. This paper proposes an algorithm to solve the redundant block problem, and gives the conditions to ensure the accurate recovery of the algorithm. On the basis of the multi-measurement vector (multiple measurement vectors,MMV) model, the algorithm proposed in this paper can process multiple samples at the same time. Finally, the experiments of face recognition show that the proposed algorithm is effective. In this paper, a weighted L _ 2N _ 1 minimization method is proposed to minimize the partial support information of the sparse signal. This method can take advantage of the correlation between frame and frame in the signal sequence and use the support information of the previous frame as the prior information of the signal of the next frame, which makes it possible to further reduce the number of samples. The error upper bound between the recovered signal and the original signal is given by using RIP,. In addition, because the two-dimensional signal is treated as matrix instead of vectorization, the running time is greatly reduced. The effectiveness of the algorithm is verified by the experiment of restoring Larynx image sequence. 4. 4. Aiming at the greedy block coordinate descent algorithm (greedy block coordinate descent,GBCD), the performance of the algorithm is analyzed by using RIP theory under additive noise and multiplicative noise interference. A sufficient condition is given to guarantee the accurate restoration of the support set of the original signal by the GBCD algorithm, and an example of satisfying the sufficient condition is given, the upper bound of the sufficient condition is discussed, and it is pointed out that if the sufficient condition is not satisfied, There exists the situation that the GBCD algorithm can not recover accurately. Finally, the performance of GBCD algorithm is verified by simulation experiments.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.7
【參考文獻(xiàn)】
相關(guān)期刊論文 前10條
1 蔡澤民;賴劍煌;;一種基于超完備字典學(xué)習(xí)的圖像去噪方法[J];電子學(xué)報(bào);2009年02期
2 石光明;劉丹華;高大化;劉哲;林杰;王良君;;壓縮感知理論及其研究進(jìn)展[J];電子學(xué)報(bào);2009年05期
3 焦李成;楊淑媛;劉芳;侯彪;;壓縮感知回顧與展望[J];電子學(xué)報(bào);2011年07期
4 金堅(jiān);谷源濤;梅順良;;壓縮采樣技術(shù)及其應(yīng)用[J];電子與信息學(xué)報(bào);2010年02期
5 林波;張?jiān)鲚x;朱炬波;;基于壓縮感知的DOA估計(jì)稀疏化模型與性能分析[J];電子與信息學(xué)報(bào);2014年03期
6 戴瓊海;付長(zhǎng)軍;季向陽(yáng);;壓縮感知研究[J];計(jì)算機(jī)學(xué)報(bào);2011年03期
7 Elaine T.Hale;;FIXED-POINT CONTINUATION APPLIED TO COMPRESSED SENSING:IMPLEMENTATION AND NUMERICAL EXPERIMENTS[J];Journal of Computational Mathematics;2010年02期
8 張春梅;尹忠科;肖明霞;;基于冗余字典的信號(hào)超完備表示與稀疏分解[J];科學(xué)通報(bào);2006年06期
9 李樹濤;魏丹;;壓縮傳感綜述[J];自動(dòng)化學(xué)報(bào);2009年11期
10 黃會(huì)營(yíng);李小光;洪俊芳;;快速定點(diǎn)獨(dú)立向量分析在語(yǔ)音信號(hào)盲分離中的應(yīng)用[J];河南師范大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年06期
相關(guān)博士學(xué)位論文 前4條
1 楊斌;像素級(jí)多傳感器圖像融合新方法研究[D];湖南大學(xué);2010年
2 鄒健;分塊稀疏表示的理論及算法研究[D];華南理工大學(xué);2012年
3 曾春艷;匹配追蹤的最佳原子選擇策略和壓縮感知盲稀疏度重建算法改進(jìn)[D];華南理工大學(xué);2013年
4 章啟恒;壓縮感知中優(yōu)化投影矩陣的研究[D];華南理工大學(xué);2013年
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