本文選題：壓縮感知 + 貪婪算法��； 參考：《西南交通大學(xué)》2014年博士論文

【摘要】：面對(duì)人類對(duì)數(shù)據(jù)需求的日益增長(zhǎng),以香農(nóng)—奈奎斯特采樣定理為基礎(chǔ)的信號(hào)處理框架,不可避免給信息系統(tǒng)的信號(hào)處理能力與硬件實(shí)現(xiàn)帶來(lái)了極大的挑戰(zhàn)。近年來(lái),一種新的利用信號(hào)的稀疏或可壓縮的先驗(yàn)特性的信號(hào)采集和壓縮理論——壓縮感知理論被提出,并受到了學(xué)術(shù)界和工業(yè)界的廣泛關(guān)注。在壓縮感知框架下,使用遠(yuǎn)低于傳統(tǒng)的奈奎斯特采樣頻率的速率去采樣先驗(yàn)稀疏或可壓縮的信號(hào),其最大的特點(diǎn)是采樣與壓縮同步進(jìn)行,因此能夠有效降低數(shù)據(jù)的傳輸量和存貯量。壓縮感知理論的研究涉及到信號(hào)的稀疏重建算法、稀疏表示以及觀測(cè)矩陣的設(shè)計(jì)。信號(hào)的稀疏重建算法主要實(shí)現(xiàn)對(duì)信號(hào)快速準(zhǔn)確的重建。稀疏表示的目標(biāo)是尋找一個(gè)合適的基,在此基下信號(hào)能夠使用少量的系數(shù)來(lái)揭示有用的信息。觀測(cè)矩陣的設(shè)計(jì)涉及約束等距性質(zhì)、非相干特性等要求。本文以壓縮感知為核心,重點(diǎn)圍繞盲稀疏度下信號(hào)的重建,以及壓縮感知與輪廓波的結(jié)合等問(wèn)題進(jìn)行研究,主要貢獻(xiàn)和創(chuàng)新工作如下：(1)可變步長(zhǎng)分階段自適應(yīng)匹配追蹤算法考慮到恢復(fù)未知信號(hào)時(shí),其稀疏度不能提前知曉這個(gè)實(shí)際問(wèn)題,對(duì)盲稀疏度下信號(hào)的重建進(jìn)行研究,系統(tǒng)總結(jié)了匹配追蹤類算法,深入分析了具有回溯思想的匹配追蹤類算法。針對(duì)自適應(yīng)匹配追蹤算法用于重建二維圖像時(shí)對(duì)步長(zhǎng)敏感的問(wèn)題,提出了可變步長(zhǎng)的分階段自適應(yīng)匹配追蹤算法。根據(jù)四比一法則,通過(guò)控制因子控制當(dāng)前迭代所估計(jì)的信號(hào)稀疏度。若當(dāng)前迭代所得到的信號(hào)尺寸較小時(shí),使用可變的大步長(zhǎng)；若當(dāng)前迭代估計(jì)到的信號(hào)尺寸較大時(shí),使用不變的步長(zhǎng)。隨著迭代的進(jìn)行,稀疏度將逐步逼近真實(shí)值。實(shí)驗(yàn)仿真表明,該方法不僅克服了步長(zhǎng)對(duì)重建質(zhì)量的影響,而且提高了圖像的峰值信噪比。(2)基于能量的固定步長(zhǎng)的自適應(yīng)匹配追蹤算法針對(duì)匹配追蹤算法對(duì)二進(jìn)制稀疏信號(hào)成功重建率較低的問(wèn)題,從數(shù)學(xué)角度證明了觀測(cè)值和原始信號(hào)之間能量的關(guān)系,在此基礎(chǔ)上提出基于能量的固定步長(zhǎng)的自適應(yīng)匹配追蹤算法。通過(guò)將觀測(cè)值的能量引入到信號(hào)重建過(guò)程中,并根據(jù)觀測(cè)值和候選信號(hào)能量之間的關(guān)系判斷是否使用步長(zhǎng)去增加當(dāng)前估計(jì)到的稀疏度,以達(dá)到通過(guò)迭代實(shí)現(xiàn)估計(jì)的稀疏度逐步逼近真實(shí)值的目的。通過(guò)實(shí)驗(yàn)仿真驗(yàn)證了該算法對(duì)二進(jìn)制稀疏信號(hào)具有較高的成功重建率,較少的重建時(shí)間以及迭代次數(shù)。(3)基于能量的可變步長(zhǎng)的白適應(yīng)匹配追蹤算法為了提高基于能量的固定步長(zhǎng)匹配追蹤算法的自適應(yīng)性,提出可變步長(zhǎng)的能量自適應(yīng)匹配追蹤算法。根據(jù)當(dāng)前的候選信號(hào)與觀測(cè)值能量之間的關(guān)系,將重建過(guò)程分為三個(gè)階段,通過(guò)兩者之間能量的大小自主選擇每次迭代所采用的步長(zhǎng)。實(shí)驗(yàn)仿真表明該算法在成功重建的頻率,重建時(shí)間以及迭代次數(shù)方面均優(yōu)于其他相比較的追蹤類算法,并從數(shù)學(xué)角度證明了步長(zhǎng)與稀疏度之間的關(guān)系以及重建階段的完整性和有序性。該算法的提出進(jìn)一步擴(kuò)大了匹配追蹤算法的應(yīng)用范圍。(4)基于小波變換的輪廓波域多尺度壓縮感知方案針對(duì)使用傳統(tǒng)的壓縮感知模型采樣二維信號(hào)時(shí),所需大尺寸觀測(cè)矩陣和較大傳輸量的問(wèn)題,提出將屬于多尺度幾何分析的輪廓波與壓縮感知相結(jié)合,設(shè)計(jì)了基于小波變換的輪廓波域多尺度壓縮感知方案。該方案將小波變換引入到輪廓波域,即對(duì)輪廓波域的方向子帶使用小波變換進(jìn)行壓縮。該變換使得所需觀測(cè)的系數(shù)的維度進(jìn)一步減少,所需觀測(cè)矩陣的尺寸也必然減小,以達(dá)到降低傳輸量和計(jì)算存儲(chǔ)的開(kāi)銷,提高圖像重建質(zhì)量的目的。通過(guò)與基于曲線波的多尺度壓縮感知相比較,仿真結(jié)果表明：該算法不僅降低了傳輸量,而且在重建質(zhì)量和所需矩陣的尺寸方面都有較大的改進(jìn)。通過(guò)將本文所提出的算法與基于小波變換的多尺度壓縮感知進(jìn)行比較,驗(yàn)證了本文算法的有效性,并通過(guò)實(shí)驗(yàn)給出了本文算法的動(dòng)機(jī)。(5)基于非下采樣輪廓波的含噪圖像CS重建算法考慮到非下采樣輪廓波能夠有效去除圖像的噪聲,在壓縮感知框架下提出基于非下采樣輪廓波域的含噪圖像重建算法。通過(guò)使用光滑投影蘭德韋伯(SPL)算法重建圖像的同時(shí),在非下采樣輪廓波域使用門限操作去除噪聲。在此基礎(chǔ)上引入非局部均值濾波對(duì)重建后的圖像進(jìn)行濾波處理。仿真結(jié)果表明,該算法比基于輪廓波域的SPL算法具有更好的重建效果和去噪能力。
[Abstract]:In the face of the growing demand for data, the signal processing framework based on Shannon Nyquist sampling theorem inevitably brings great challenges to the signal processing capability and hardware implementation of the information system. In recent years, a new theory of signal acquisition and compression using sparse or compressible prior characteristics of signals is proposed. Compression perception theory has been proposed and received extensive attention from academia and industry. Under the framework of compressed sensing, the prior sparse or compressible signals are sampled at a much lower rate than the traditional Nyquist sampling rate. The greatest feature is that sampling and compression are carried out in the same step, and thus the transmission of data can be effectively reduced. The research of compressed sensing theory involves sparse reconstruction of signals, sparse representation and the design of observation matrices. The sparse reconstruction algorithm of the signal mainly realizes the rapid and accurate reconstruction of the signal. The target of the sparse representation is to find a suitable base. Under this basis, the signal can use a small number of coefficients to reveal the usefulness. Information. The design of the observation matrix involves constraint equidistance properties, non coherent characteristics and so on. This paper focuses on compressed sensing as the core, focusing on the reconstruction of signals under blind sparsity, and the combination of compressed sensing and contour waves. The main contributions and innovations are as follows: (1) variable step size adaptive matching tracking algorithm Considering that the unknown signal is restored, the sparsity of the method can not be known in advance, and the reconstruction of the signal under blind sparsity is studied. The matching pursuit class algorithm is summarized, and the matching tracking algorithm with backtracking is deeply analyzed. The adaptive matching tracking algorithm is sensitive to the step size for the reconstruction of the two-dimensional image. A phased adaptive matching tracking algorithm with variable step size is proposed. According to the four to one rule, the signal sparsity estimated by the current iteration is controlled by the control factor. If the signal size obtained by the current iteration is smaller, a variable large step is used; if the current iteration is estimated to be larger, the invariant is used. Step size. With the iteration, the sparsity will gradually approach the real value. Experimental simulation shows that the method not only overcomes the effect of the step size on the reconstruction quality, but also improves the peak signal to noise ratio of the image. (2) the adaptive matching tracking algorithm based on the fixed step length based on energy is successfully reconstructed for the binary sparse signal. The relationship between the observed value and the energy of the original signal is proved mathematically. On this basis, an adaptive matching tracking algorithm based on the energy based fixed step length is proposed. By introducing the energy of the observed value into the process of the signal reconstruction, and judging whether it is used according to the relationship between the observed value and the energy of the candidate signal. The step length increases the sparsity of the estimated current to achieve the goal of gradual approximation of the true value by iterative realization of the estimated sparsity. The experimental simulation shows that the algorithm has a high successful reconstruction rate for binary sparse signals, less reconstruction time and iteration times. (3) the white adaptation matching based on the variable step size of energy. In order to improve the adaptability of the fixed step matching tracking algorithm based on energy, the tracking algorithm proposes a variable step size adaptive matching tracking algorithm. According to the relationship between the current candidate signal and the observation energy, the reconstruction process is divided into three stages, and each iteration is selected independently by the size of the energy between the two. The experimental simulation shows that the algorithm is better than the other tracking algorithms in the frequency of successful reconstruction, the time of reconstruction and the number of iterations. The relationship between the step length and the sparsity and the integrity and order of the reconstruction phase are proved from the mathematical point of view. The proposed algorithm further expands the matching tracking algorithm. The application scope of the method. (4) the multiscale compression perception scheme based on the wavelet transform based contours domain is designed to solve the problem of large size observation matrix and large transmission amount when using the traditional compressed sensing model to sample the two-dimensional signal. This scheme introduces the wavelet transform into the contour domain, that is, the wavelet transform is used to compress the direction subband of the contour wave domain. This transform makes the dimensions of the measured coefficients further reduced, and the size of the observed matrix is also reduced, in order to reduce the amount of transmission and calculate storage. By comparing with the multiscale compression based on curve wave, the simulation results show that the algorithm not only reduces the amount of transmission, but also improves the quality of reconstruction and the size of the required matrix. By the algorithm proposed in this paper and the multiscale compression based on the wavelet transform The effectiveness of this algorithm is verified by comparison, and the motivation of this algorithm is given through experiments. (5) the CS reconstruction algorithm based on non down sampled contours is considered to be able to effectively remove the noise of the image by non down sampling contour waves, and proposes a noisy image based on the non down sampling contour domain under the compressed sensing framework. Reconstruction algorithm. By using the smooth projection lander Weber (SPL) algorithm to reconstruct the image, the threshold operation is used to remove the noise in the non lower sampling contour domain. On this basis, the non local mean filter is used to filter the reconstructed image. The simulation results show that the algorithm is better than the SPL algorithm based on the contour domain. Reconstruction effect and de-noising ability.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.7

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