基于結構稀疏性的信號頻譜估計算法研究
發(fā)布時間：2018-12-11 06:49
【摘要】：壓縮感知打破傳統(tǒng)的采樣定理，利用信號的稀疏性，能夠用較少的采樣點數精確地恢復原始信號。對于近幾年提出的結構稀疏信號受到廣泛關注，其變換域的非零元素聚集分布，利用其信號分布特點能達到更好的頻譜估計效果，但是往往忽略了信號在結構內部的稀疏問題，本文在上述理論的研究基礎上，對結構內稀疏的信號頻譜估計算法進行了深入研究。 首先，本文對壓縮感知理論框架及主要內容進行深入研究。包括觀測矩陣、稀疏矩陣設計、信號重構算法以及壓縮感知中的一些重要定理：受限等距性質和不相關定理，并且就結構稀疏信號的分布特點進行研究。 其次，傳統(tǒng)的結構稀疏優(yōu)化問題將信號的結構特點作為先驗知識對信號進行重構，但是沒有考慮頻率表示失配的問題，在充分研究信號結構特點和信號稀疏性的基礎上，提出基于分塊結構和冗余框架的信號估計算法，該算法將冗余框架引入group-lasso算法估計信號和頻率占用頻段，結合相干抑制模型和頻率插值進行頻譜估計。實驗結果表明，由于融合了冗余框架和信號的結構分布特點，本文所提算法對頻率失配的塊結構信號的重構和頻率估計在魯棒性和重構精度上都優(yōu)于傳統(tǒng)的信號估計算法。 最后，對于塊稀疏信號，，利用信號的分塊特性能降低信號采樣率，但是往往忽略塊內稀疏的問題。在處理隨機信號時，根據復指數的旋轉不變性，將冗余字典做極坐標插值映射到超球面，對整個頻域進行處理，信號和頻譜估計精度高，但運行時間太長。在此基礎上，本文提出基于極坐標插值的塊結構稀疏信號頻譜估計，將信號的分塊特性與極坐標插值相結合，先去除非零頻塊，降低計算復雜度。實驗結果表明，本文所提算法可有效減少計算時間和估計誤差且魯棒性較好。
[Abstract]:Compression sensing breaks the traditional sampling theorem and can accurately recover the original signal with less sampling points by using the sparsity of the signal. For the structural sparse signal proposed in recent years, widespread attention has been paid to the non-zero element aggregation distribution in the transform domain. Using the characteristics of the signal distribution, a better spectrum estimation effect can be achieved, but the sparse problem of the signal within the structure is often ignored. Based on the above theory, the sparse signal spectrum estimation algorithm in the structure is studied in this paper. First of all, the theoretical framework and main contents of compressed perception are deeply studied in this paper. It includes observation matrix, sparse matrix design, signal reconstruction algorithm and some important theorems in compression perception: restricted equidistant property and non-correlation theorem. The distribution characteristics of structural sparse signals are also studied. Secondly, the traditional structural sparse optimization problem uses the structural characteristics of the signal as a priori knowledge to reconstruct the signal, but does not consider the problem of frequency representation mismatch, on the basis of fully studying the signal structural characteristics and signal sparsity. A signal estimation algorithm based on block structure and redundant frame is proposed. The redundant frame is introduced into the group-lasso algorithm to estimate the signal and frequency occupation band, and the coherent suppression model and frequency interpolation are combined to estimate the frequency spectrum. The experimental results show that the proposed algorithm is more robust and accurate than the traditional signal estimation algorithm for the reconstruction and frequency estimation of the block structure signals with frequency mismatch due to the combination of the redundant frame and the structural distribution of the signals. Finally, for block sparse signals, the signal sampling rate can be reduced by using the blocking characteristics of the signals, but the problem of block sparsity is often ignored. According to the rotation invariance of complex exponent, the redundant dictionaries are interpolated to hypersphere by polar coordinates. The whole frequency domain is processed. The precision of signal and spectrum estimation is high, but the running time is too long. On this basis, this paper presents the spectral estimation of block structure sparse signal based on polar interpolation, which combines the blocking characteristic of the signal with polar interpolation, and reduces the computational complexity by removing the zero frequency block first. The experimental results show that the proposed algorithm can effectively reduce the computation time and estimate error, and the robustness is good.
【學位授予單位】：燕山大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.23
本文編號：2372088
[Abstract]:Compression sensing breaks the traditional sampling theorem and can accurately recover the original signal with less sampling points by using the sparsity of the signal. For the structural sparse signal proposed in recent years, widespread attention has been paid to the non-zero element aggregation distribution in the transform domain. Using the characteristics of the signal distribution, a better spectrum estimation effect can be achieved, but the sparse problem of the signal within the structure is often ignored. Based on the above theory, the sparse signal spectrum estimation algorithm in the structure is studied in this paper. First of all, the theoretical framework and main contents of compressed perception are deeply studied in this paper. It includes observation matrix, sparse matrix design, signal reconstruction algorithm and some important theorems in compression perception: restricted equidistant property and non-correlation theorem. The distribution characteristics of structural sparse signals are also studied. Secondly, the traditional structural sparse optimization problem uses the structural characteristics of the signal as a priori knowledge to reconstruct the signal, but does not consider the problem of frequency representation mismatch, on the basis of fully studying the signal structural characteristics and signal sparsity. A signal estimation algorithm based on block structure and redundant frame is proposed. The redundant frame is introduced into the group-lasso algorithm to estimate the signal and frequency occupation band, and the coherent suppression model and frequency interpolation are combined to estimate the frequency spectrum. The experimental results show that the proposed algorithm is more robust and accurate than the traditional signal estimation algorithm for the reconstruction and frequency estimation of the block structure signals with frequency mismatch due to the combination of the redundant frame and the structural distribution of the signals. Finally, for block sparse signals, the signal sampling rate can be reduced by using the blocking characteristics of the signals, but the problem of block sparsity is often ignored. According to the rotation invariance of complex exponent, the redundant dictionaries are interpolated to hypersphere by polar coordinates. The whole frequency domain is processed. The precision of signal and spectrum estimation is high, but the running time is too long. On this basis, this paper presents the spectral estimation of block structure sparse signal based on polar interpolation, which combines the blocking characteristic of the signal with polar interpolation, and reduces the computational complexity by removing the zero frequency block first. The experimental results show that the proposed algorithm can effectively reduce the computation time and estimate error, and the robustness is good.
【學位授予單位】：燕山大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN911.23
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