【摘要】：壓縮感知打破傳統(tǒng)的采樣定理，利用信號(hào)的稀疏性，能夠用較少的采樣點(diǎn)數(shù)精確地恢復(fù)原始信號(hào)。對(duì)于近幾年提出的結(jié)構(gòu)稀疏信號(hào)受到廣泛關(guān)注，其變換域的非零元素聚集分布，利用其信號(hào)分布特點(diǎn)能達(dá)到更好的頻譜估計(jì)效果，但是往往忽略了信號(hào)在結(jié)構(gòu)內(nèi)部的稀疏問題，本文在上述理論的研究基礎(chǔ)上，對(duì)結(jié)構(gòu)內(nèi)稀疏的信號(hào)頻譜估計(jì)算法進(jìn)行了深入研究。 首先，本文對(duì)壓縮感知理論框架及主要內(nèi)容進(jìn)行深入研究。包括觀測(cè)矩陣、稀疏矩陣設(shè)計(jì)、信號(hào)重構(gòu)算法以及壓縮感知中的一些重要定理：受限等距性質(zhì)和不相關(guān)定理，并且就結(jié)構(gòu)稀疏信號(hào)的分布特點(diǎn)進(jìn)行研究。 其次，傳統(tǒng)的結(jié)構(gòu)稀疏優(yōu)化問題將信號(hào)的結(jié)構(gòu)特點(diǎn)作為先驗(yàn)知識(shí)對(duì)信號(hào)進(jìn)行重構(gòu)，但是沒有考慮頻率表示失配的問題，在充分研究信號(hào)結(jié)構(gòu)特點(diǎn)和信號(hào)稀疏性的基礎(chǔ)上，提出基于分塊結(jié)構(gòu)和冗余框架的信號(hào)估計(jì)算法，該算法將冗余框架引入group-lasso算法估計(jì)信號(hào)和頻率占用頻段，結(jié)合相干抑制模型和頻率插值進(jìn)行頻譜估計(jì)。實(shí)驗(yàn)結(jié)果表明，由于融合了冗余框架和信號(hào)的結(jié)構(gòu)分布特點(diǎn)，本文所提算法對(duì)頻率失配的塊結(jié)構(gòu)信號(hào)的重構(gòu)和頻率估計(jì)在魯棒性和重構(gòu)精度上都優(yōu)于傳統(tǒng)的信號(hào)估計(jì)算法。 最后，對(duì)于塊稀疏信號(hào)，，利用信號(hào)的分塊特性能降低信號(hào)采樣率，但是往往忽略塊內(nèi)稀疏的問題。在處理隨機(jī)信號(hào)時(shí)，根據(jù)復(fù)指數(shù)的旋轉(zhuǎn)不變性，將冗余字典做極坐標(biāo)插值映射到超球面，對(duì)整個(gè)頻域進(jìn)行處理，信號(hào)和頻譜估計(jì)精度高，但運(yùn)行時(shí)間太長(zhǎng)。在此基礎(chǔ)上，本文提出基于極坐標(biāo)插值的塊結(jié)構(gòu)稀疏信號(hào)頻譜估計(jì)，將信號(hào)的分塊特性與極坐標(biāo)插值相結(jié)合，先去除非零頻塊，降低計(jì)算復(fù)雜度。實(shí)驗(yàn)結(jié)果表明，本文所提算法可有效減少計(jì)算時(shí)間和估計(jì)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(xué)位授予單位】：燕山大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.23

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