【摘要】：近十年來,壓縮感知理論(compressed sensing)成為信號(hào)處理方向的熱門研究方向,CS理論解決了傳統(tǒng)采樣機(jī)制中采樣率高的難題,可以大大減少資源的浪費(fèi),僅需少量采樣值即可在接收端精確或近似地重構(gòu)原始信號(hào)。語(yǔ)音信號(hào)具有稀疏性,而如果通過引入壓縮感知技術(shù),將其和語(yǔ)音信號(hào)處理結(jié)合,這將會(huì)給語(yǔ)音信號(hào)處理領(lǐng)域帶來新的發(fā)展。本文的研究就是基于這個(gè)前提,針對(duì)在實(shí)際的應(yīng)用中語(yǔ)音壓縮感知系統(tǒng)必然含有噪聲,主要考慮CS系統(tǒng)中稀疏表示和觀測(cè)矩陣的部分來研究消噪技術(shù),以提升系統(tǒng)魯棒性。本學(xué)位論文的研究?jī)?nèi)容和創(chuàng)新點(diǎn)如下:首先,詳細(xì)闡述了關(guān)于壓縮感知理論的研究背景知識(shí),概括了壓縮感知理論發(fā)展的數(shù)十年來各種關(guān)鍵技術(shù)的研究現(xiàn)狀,總結(jié)性地介紹了語(yǔ)音壓縮感知技術(shù)的應(yīng)用與發(fā)展,本團(tuán)隊(duì)在前期的工作成果等。其次,從壓縮感知理論涉及的稀疏基、觀測(cè)矩陣和重構(gòu)算法三個(gè)核心技術(shù)方面來詳細(xì)地介紹。然后,重點(diǎn)對(duì)語(yǔ)音信號(hào)的特征進(jìn)行研究,經(jīng)過一系列的仿真實(shí)驗(yàn),證實(shí)了將CS技術(shù)應(yīng)用于語(yǔ)音信號(hào)處理中是可行的。最后,考察了含噪語(yǔ)音在壓縮感知系統(tǒng)中的性能,以及噪聲對(duì)CS系統(tǒng)各部分的影響。正是建立在這些研究的前提之上,本論文提出了一種基于FIST算法的改進(jìn)K-SVD字典學(xué)習(xí)方法。通過將快速迭代收縮閾值算法引入字典訓(xùn)練過程,提出了基于快速迭代收縮閾值算法的K-SVD字典學(xué)習(xí)算法。該算法首先用快速迭代收縮閾值算法來完成K-SVD字典學(xué)習(xí)算法的稀疏編碼階段,更新字典則使用K-SVD的經(jīng)典更新方法,稀疏編碼和字典更新兩步迭代學(xué)習(xí)得到新的字典。將其訓(xùn)練出的字典對(duì)語(yǔ)音信號(hào)進(jìn)行稀疏化,再觀測(cè)重構(gòu),并將此算法應(yīng)用于語(yǔ)音信號(hào)的壓縮感知過程。結(jié)果表明本文算法比經(jīng)典的K-SVD算法字典訓(xùn)練速度快、RMSE低。進(jìn)一步考察算法的語(yǔ)音去噪能力,在白噪聲環(huán)境下并考察不同字典參數(shù)時(shí)的字典性能,實(shí)驗(yàn)結(jié)果表明本文算法比經(jīng)典的K-SVD算法獲得更高的輸出信噪比,具有良好的去噪性能。最后,本文提出了一種設(shè)計(jì)最佳投影和獲得學(xué)習(xí)字典的聯(lián)合設(shè)計(jì)方法,以此來提升壓縮感知應(yīng)用中的重構(gòu)和消噪性能。基于對(duì)一個(gè)給定的字典存在封閉的表達(dá)形式的前提,對(duì)字典SVD分解,通過數(shù)學(xué)推導(dǎo)得到投影矩陣的表達(dá)式,此時(shí)投影矩陣和字典相乘是一個(gè)Parseval緊框架。設(shè)計(jì)得到的最佳投影矩陣可以通過字典得到。仿真結(jié)果顯示,與其他方法相比,本文提出的設(shè)計(jì)方法應(yīng)用于語(yǔ)音信號(hào)有較好的消噪性能。
[Abstract]:In the past ten years, the compressed sensing theory (compressed sensing) has become a hot research direction in signal processing. CS theory solves the problem of high sampling rate in traditional sampling mechanism, and can greatly reduce the waste of resources. The original signal can be reconstructed accurately or approximately at the receiver with only a few sampling values. Speech signal is sparse, but if compression sensing technology is introduced and combined with speech signal processing, it will bring new development to the field of speech signal processing. The research of this paper is based on this premise. In order to improve the robustness of the CS system, the sparse representation and the observation matrix are considered in order to improve the robustness of the system. The research contents and innovations of this dissertation are as follows: firstly, the background knowledge of the theory of compressed perception is described in detail, and the research status of various key technologies in the development of the theory of compressed perception is summarized. This paper summarizes the application and development of speech compression perception technology, the team's previous work and so on. Secondly, the sparse basis, observation matrix and reconstruction algorithm of compressed sensing theory are introduced in detail. After a series of simulation experiments, it is proved that it is feasible to apply CS technology to speech signal processing. Finally, the performance of noisy speech in compression sensing system and the effect of noise on each part of CS system are investigated. Based on these researches, this paper proposes an improved K-SVD dictionary learning method based on FIST algorithm. By introducing the fast iterative shrinkage threshold algorithm into the dictionary training process, a K-SVD dictionary learning algorithm based on the fast iterative contraction threshold algorithm is proposed. The algorithm uses the fast iterative shrinkage threshold algorithm to complete the sparse coding phase of the K-SVD dictionary learning algorithm, and the update dictionary uses K-SVD 's classical updating method, sparse coding and dictionary updating two-step iterative learning to obtain the new dictionary. The dictionary is used to sparse the speech signal, and then the algorithm is applied to the process of speech signal compression and perception. The results show that the proposed algorithm is faster than the classical K-SVD algorithm in dictionary training speed and lower in RMSE. Furthermore, the speech denoising ability of the algorithm and the dictionary performance under white noise and different dictionary parameters are investigated. The experimental results show that the proposed algorithm has higher output SNR than the classical K-SVD algorithm. It has good denoising performance. Finally, a joint design method of optimal projection and learning dictionary is proposed to improve the performance of reconstruction and de-noising in compression sensing applications. Based on the premise that there is a closed representation for a given dictionary, the SVD decomposition of the dictionary is used to derive the expression of the projection matrix by mathematical derivation. In this case, the multiplying of the projection matrix and the dictionary is a Parseval compact frame. The optimal projection matrix can be obtained by dictionary. The simulation results show that compared with other methods, the proposed design method has better denoising performance.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TN912.3

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