本文選題：壓縮感知 + 塊稀疏信號(hào)　； 參考：《湘潭大學(xué)》2014年碩士論文

【摘要】：近年來(lái)，壓縮感知（Compressed Sensing,CS）理論的研究受到越來(lái)越多學(xué)者的關(guān)注，它突破了信號(hào)處理領(lǐng)域中傳統(tǒng)的香農(nóng)/奈奎斯特（Shannon/Nyquist）采樣定理的采樣限定，大大降低了采樣數(shù)據(jù)量，在醫(yī)學(xué)影像、圖像處理、雷達(dá)探測(cè)、模式識(shí)別等領(lǐng)域得到了廣泛的應(yīng)用。壓縮感知理論的一個(gè)重要任務(wù)是對(duì)壓縮采樣后的信號(hào)進(jìn)行重構(gòu)，這些信號(hào)都是稀疏或可稀疏化的，即信號(hào)中只有少量元素是非零的，且非零元素的位置是隨機(jī)的。但是實(shí)際中大部分信號(hào)具有一定的內(nèi)在結(jié)構(gòu)，，近幾年非零元素成塊出現(xiàn)的塊稀疏信號(hào)成為壓縮感知理論的研究熱點(diǎn)。 本文從壓縮感知理論出發(fā)，對(duì)壓縮感知塊稀疏信號(hào)重構(gòu)算法進(jìn)行了研究。我們首先詳細(xì)介紹了標(biāo)準(zhǔn)塊稀疏信號(hào)重構(gòu)算法混合l2/l1范式最小化問(wèn)題（Mixedl2/l1NormOptimization Program,L-OPT）、塊匹配追蹤算法（Block matching pursuit,BMP）、塊正交匹配追蹤（Block orthogonal matching pursuit, BOMP）算法。通過(guò)對(duì)標(biāo)準(zhǔn)的塊稀疏信號(hào)的重構(gòu)算法進(jìn)行分析討論，我們對(duì)當(dāng)前廣泛使用的塊正交匹配追蹤算法的若干不足進(jìn)行改進(jìn)，提出了三個(gè)改進(jìn)的塊正交匹配追蹤算法，分別為基于前向預(yù)測(cè)策略的塊正交匹配追蹤算法（LABOMP）、基于正交投影的塊正交匹配追蹤算法（PBOMP）以及結(jié)合前兩者提出的改進(jìn)算法（PLABOMP）。其中LABOMP算法是針對(duì)BOMP算法在迭代選擇原子塊的過(guò)程中，每次選擇當(dāng)次迭代最優(yōu)的原子塊，并不能保證最終迭代性能是最優(yōu)的問(wèn)題，提出的在每次迭代過(guò)程中通過(guò)預(yù)測(cè)原子塊在未來(lái)迭代過(guò)程中的性能來(lái)選擇最優(yōu)原子塊的算法；PBOMP算法是針對(duì)運(yùn)用內(nèi)積準(zhǔn)則選擇原子塊的算法得不到最優(yōu)原子塊的缺陷，提出的運(yùn)用正交投影策略來(lái)選擇更加適宜的原子塊的算法；PLABOMP算法是結(jié)合前兩者平衡時(shí)間復(fù)雜度和精度的改進(jìn)算法。通過(guò)對(duì)比實(shí)驗(yàn)可知，本文提出的若干算法較BOMP算法在精度和復(fù)雜度方面均有所改進(jìn)。 塊稀疏重構(gòu)算法中沒(méi)有一種權(quán)威的算法能保證重構(gòu)精度、時(shí)間復(fù)雜度等性能都優(yōu)于其他算法。本文針對(duì)各種塊稀疏重構(gòu)算法的不足，提出了基于融合的塊稀疏重構(gòu)算法（BlockFA），該算法將參與融合的各個(gè)算法得到的信號(hào)估計(jì)進(jìn)行融合得到最后的估計(jì)信號(hào)。其主要優(yōu)勢(shì)在于參與融合的每個(gè)算法都無(wú)需任何較大的修改就能進(jìn)行，且結(jié)合了現(xiàn)有不同的塊稀疏重構(gòu)算法的優(yōu)勢(shì)，得到新的重構(gòu)算法的重構(gòu)精度不低于任何參與融合的算法。
[Abstract]:In recent years, the research of compressed sensing CS (CS) theory has been paid more and more attention by more and more scholars. It breaks through the sampling limitation of the traditional Shannon / Nyquist sampling theorem in the field of signal processing, and greatly reduces the amount of sampling data in medical images. Image processing, radar detection, pattern recognition and other fields have been widely used. One of the important tasks of compression sensing theory is to reconstruct the compressed sampled signals, which are sparse or sparse, that is, only a few elements in the signal are non-zero, and the position of the non-zero elements is random. However, most of the signals have a certain internal structure in practice. In recent years, block sparse signals with non-zero elements have become the research focus of compression sensing theory. Based on the theory of compressed sensing, the algorithm of sparse signal reconstruction of compressed perceptual blocks is studied in this paper. We first introduce the standard block sparse signal reconstruction algorithm, the mixed l2/l1 normal minimization problem (Mixedl2 / L1 Norm Optimization Programms-OPT), the Block matching tracking algorithm (BMP), and the Block orthogonal matching pursuit, tracking (BMP) algorithm. Through the analysis and discussion of the standard block sparse signal reconstruction algorithm, we improve some shortcomings of the current block orthogonal matching tracking algorithm, and propose three improved block orthogonal matching tracking algorithms. They are block orthogonal matching tracking algorithm (LABOMP) based on forward prediction strategy, block orthogonal matching tracking algorithm (PBOMP) based on orthogonal projection and improved algorithm (PLABMP) combined with the former two algorithms. The LABOMP algorithm can not guarantee that the final iteration performance is optimal when selecting the best atomic block in the process of iterative selection of atomic block. The algorithm proposed to select the optimal atomic block in each iteration process by predicting the performance of atomic block in the future iteration process is aimed at the defect that the algorithm using the inner product criterion to select the atomic block can not get the optimal atomic block. The proposed algorithm, which uses orthogonal projection strategy to select more suitable atomic blocks, is an improved algorithm which combines the former two algorithms to balance time complexity and precision. The comparison experiments show that the proposed algorithms are better in accuracy and complexity than the BOMP algorithm. There is no authoritative algorithm in block sparse reconstruction algorithm which can guarantee the reconstruction accuracy and time complexity. In this paper, a block sparse reconstruction algorithm based on fusion (BlockFA) is proposed to overcome the shortcomings of various block sparse reconstruction algorithms. Its main advantage is that each algorithm involved in the fusion can be implemented without any big modification, and combining the advantages of the existing block sparse reconstruction algorithm, the reconstruction accuracy of the new reconstruction algorithm is no less than that of any other fusion algorithm.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.7

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