基于小波模極大值點的信號稀疏表示及壓縮感知重構
發(fā)布時間：2018-08-27 14:39
【摘要】：隨著信息技術的飛速發(fā)展,傳統(tǒng)的Shannon/Nyquist采樣定理已不能滿足日益增長的海量數(shù)據(jù)的存儲、傳輸、處理等問題,這就需要更強大更高速的信號處理理論和算法,也需要進一步提升硬件設備的信號處理能力。近年來,Candes、Donoho和華裔數(shù)學家Tao等人提出了一種新的信息獲取理論——壓縮感知理論(Compressed Sensing,CS)。該理論的本質為可壓縮信號(在某個基上具有稀疏描述)的少量隨機線性投影就包含了該信號重構和處理的隨機信息,也就是僅僅利用信號稀疏或可壓縮的先驗知識和少量全局線性測量就可以獲得信號的精確重建。 稀疏表示和恢復算法一直是壓縮感知理論的核心內容,因此,本文圍繞稀疏表示和重構算法問題做了以下幾方面的工作： 1簡單介紹了壓縮感知理論的基本框架和流程,針對壓縮感知理論中信號的稀疏表示、觀測矩陣的設計以及信號的重構算法等核心問題進行了詳細分析,闡述了壓縮感知理論的初步應用,為本文的算法研究奠定了理論基礎。 2針對信號的稀疏表示問題,本文提出了基于小波模極大值搜索的信號稀疏表示方法,以及對應的信號重構算法。首先,該方法在小波變換的基礎上,尋找各層小波系數(shù)的模極大值點,并根據(jù)模極大值點的傳播特性對其進一步優(yōu)化處理,使得信號的稀疏性得到顯著提高。然后,將稀疏化的信號通過觀測矩陣得到它的觀測值,對觀測值進行熵編碼以實現(xiàn)數(shù)據(jù)壓縮傳輸。解碼時,采用正交匹配追蹤算法得到模極大值點的估計值,最后用交替投影算法重構出原始信號。仿真結果表明,與經(jīng)典壓縮感知算法相比,該算法的信號重構質量有較大提高,且由于稀疏度增大,信號具有更好的可壓縮性,實驗表明本文算法對復雜信號效果更明顯。 3針對二維信號的重構問題,本文對基于小波域樹形結構的回溯正交匹配追蹤算法(TBOMP)的搜索小波子樹的部分進行改進,根據(jù)小波樹形結構的特點,結合貪婪樹逼近,提出了倒置小波子樹搜索的方法,使搜索過程更加有效、簡單,然后通過回溯刪除的思想進一步優(yōu)化搜索結果,最后將該算法應用到二維圖像重構中。仿真結果表明,與原有同類壓縮感知算法相比,該算法的信號重構質量大大提高。
[Abstract]:With the rapid development of information technology, the traditional Shannon/Nyquist sampling theorem can not meet the growing problems of massive data storage, transmission, processing and so on, which requires more powerful and high-speed signal processing theory and algorithm. It is also necessary to further enhance the signal processing capability of hardware devices. In recent years, Candesus Donoho and Tao et al., a Chinese mathematician, have proposed a new information acquisition theory, the theory of compressed perception (Compressed Sensing,CS). The essence of this theory is that a small number of random linear projections of compressible signals (with sparse descriptions on a basis) contain random information for the reconstruction and processing of the signals. In other words, the accurate reconstruction of the signal can be obtained by using only the prior knowledge of sparse or compressible signal and a few global linear measurements. Sparse representation and restoration algorithms have always been the core of compressed sensing theory, so, In this paper, we focus on sparse representation and reconstruction algorithms in the following aspects: 1 the basic framework and flow of compressed perception theory are briefly introduced, and the sparse representation of signals in compressed sensing theory is discussed. The design of observation matrix and the algorithm of signal reconstruction are analyzed in detail, and the preliminary application of compression sensing theory is expounded, which lays a theoretical foundation for the research of the algorithm in this paper. In this paper, a signal sparse representation method based on wavelet modulus maximum search and corresponding signal reconstruction algorithm are proposed. Firstly, on the basis of wavelet transform, this method finds the modulus maximum points of wavelet coefficients in each layer, and optimizes the processing according to the propagation characteristics of the modulus maximum points, so that the sparsity of signals is improved significantly. Then, the sparse signal is obtained by the observation matrix, and the observed value is encoded by entropy to realize the data compression and transmission. In decoding, the orthogonal matching tracking algorithm is used to obtain the estimation of the modulus maximum, and the original signal is reconstructed by alternating projection algorithm. The simulation results show that compared with the classical compression sensing algorithm, the signal reconstruction quality of this algorithm is improved greatly, and the signal has better compressibility because of the increase of sparsity. Experiments show that the algorithm is more effective for complex signals. 3 aiming at the reconstruction of two-dimensional signals, this paper improves the search of wavelet subtree based on (TBOMP), a backtracking orthogonal matching algorithm based on the tree structure in wavelet domain. According to the characteristics of wavelet tree structure and greedy tree approximation, an inverted wavelet subtree search method is proposed, which makes the search process more efficient and simple. Then the search results are optimized by the idea of backtracking deletion. Finally, the algorithm is applied to 2D image reconstruction. The simulation results show that the signal reconstruction quality of this algorithm is greatly improved compared with the original similar compression sensing algorithm.
【學位授予單位】：北京交通大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.7
本文編號：2207588
[Abstract]:With the rapid development of information technology, the traditional Shannon/Nyquist sampling theorem can not meet the growing problems of massive data storage, transmission, processing and so on, which requires more powerful and high-speed signal processing theory and algorithm. It is also necessary to further enhance the signal processing capability of hardware devices. In recent years, Candesus Donoho and Tao et al., a Chinese mathematician, have proposed a new information acquisition theory, the theory of compressed perception (Compressed Sensing,CS). The essence of this theory is that a small number of random linear projections of compressible signals (with sparse descriptions on a basis) contain random information for the reconstruction and processing of the signals. In other words, the accurate reconstruction of the signal can be obtained by using only the prior knowledge of sparse or compressible signal and a few global linear measurements. Sparse representation and restoration algorithms have always been the core of compressed sensing theory, so, In this paper, we focus on sparse representation and reconstruction algorithms in the following aspects: 1 the basic framework and flow of compressed perception theory are briefly introduced, and the sparse representation of signals in compressed sensing theory is discussed. The design of observation matrix and the algorithm of signal reconstruction are analyzed in detail, and the preliminary application of compression sensing theory is expounded, which lays a theoretical foundation for the research of the algorithm in this paper. In this paper, a signal sparse representation method based on wavelet modulus maximum search and corresponding signal reconstruction algorithm are proposed. Firstly, on the basis of wavelet transform, this method finds the modulus maximum points of wavelet coefficients in each layer, and optimizes the processing according to the propagation characteristics of the modulus maximum points, so that the sparsity of signals is improved significantly. Then, the sparse signal is obtained by the observation matrix, and the observed value is encoded by entropy to realize the data compression and transmission. In decoding, the orthogonal matching tracking algorithm is used to obtain the estimation of the modulus maximum, and the original signal is reconstructed by alternating projection algorithm. The simulation results show that compared with the classical compression sensing algorithm, the signal reconstruction quality of this algorithm is improved greatly, and the signal has better compressibility because of the increase of sparsity. Experiments show that the algorithm is more effective for complex signals. 3 aiming at the reconstruction of two-dimensional signals, this paper improves the search of wavelet subtree based on (TBOMP), a backtracking orthogonal matching algorithm based on the tree structure in wavelet domain. According to the characteristics of wavelet tree structure and greedy tree approximation, an inverted wavelet subtree search method is proposed, which makes the search process more efficient and simple. Then the search results are optimized by the idea of backtracking deletion. Finally, the algorithm is applied to 2D image reconstruction. The simulation results show that the signal reconstruction quality of this algorithm is greatly improved compared with the original similar compression sensing algorithm.
【學位授予單位】：北京交通大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.7
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