【摘要】：壓縮感知是一種全新的信號處理技術(shù),它可以邊采樣邊壓縮,打破了奈奎斯特采樣定理的約束。它的采樣頻率遠(yuǎn)低于奈奎斯特采樣頻率,同時實(shí)現(xiàn)了對信號的壓縮,這大大節(jié)約了采樣資源、傳輸帶寬以及存儲空間。壓縮感知關(guān)鍵技術(shù)有三個部分:稀疏表示,觀測矩陣的構(gòu)建以及重構(gòu)算法的設(shè)計(jì)。應(yīng)用壓縮感知的前提條件是信號具有稀疏性或者是可壓縮的,而語音信號是近似稀疏的,所以可以應(yīng)用壓縮感知對語音信號進(jìn)行處理。本文研究了語音與壓縮感知的結(jié)合,并重點(diǎn)研究了語音壓縮感知的魯棒性重構(gòu)算法的設(shè)計(jì),因?yàn)轸敯粜缘闹貥?gòu)算法是壓縮感知技術(shù)能否被實(shí)際應(yīng)用的關(guān)鍵。本文的主要研究內(nèi)容和創(chuàng)新如下:首先,本文詳細(xì)介紹了壓縮感知基礎(chǔ)理論以及語音信號與壓縮感知的結(jié)合,驗(yàn)證了語音信號的稀疏性,并且通過實(shí)驗(yàn)仿真討論了現(xiàn)有的具有代表性的語音壓縮感知的觀測矩陣與重構(gòu)算法的性能。然后探討了噪聲對語音壓縮感知的各個部分的影響。其次,研究了一種新型的快速重構(gòu)算法,它與其他的算法不同,它借助了離散余弦變換(DCT)基與確定性觀測矩陣的特性,使得重構(gòu)算法的復(fù)雜度大大的降低。但是,通過實(shí)驗(yàn)發(fā)現(xiàn),這種快速重構(gòu)算法對噪聲的魯棒性能不好。因此,本文提出了一種自適應(yīng)快速重構(gòu)算法,該算法根據(jù)輸入語音信號的信噪比,自適應(yīng)的選擇最優(yōu)的重構(gòu)參數(shù)。實(shí)驗(yàn)仿真表明,自適應(yīng)的快速重構(gòu)算法具有較好的抗噪聲能力,提高了語音信號的重構(gòu)信噪比且重構(gòu)速度也有所提升。最后,分析了前向后向追蹤(FBP)算法,發(fā)現(xiàn)其固定了前向步長和后向步長,即每次迭代時支撐集增加的元素個數(shù)是固定的,這會導(dǎo)致算法的收斂速度不理想。因?yàn)樵谥貥?gòu)的過程中,殘差中含有的信號分量越來越少,因此應(yīng)該增大迭代的步長以加快算法的重構(gòu)速度。所以,本文提出了快速的前向后向追蹤(FFBP)算法,它根據(jù)兩次相鄰迭代的殘差的變化率,動態(tài)的調(diào)整前向步長,最終提高了重構(gòu)語音信號的速度。實(shí)驗(yàn)仿真表明,FFBP算法具有和FBP算法同等的重構(gòu)信噪比,但是,FFBP算法的重構(gòu)速度明顯快于FBP算法。
[Abstract]:Compression sensing is a new signal processing technology, which can compress while sampling, breaking the constraint of Nyquist sampling theorem. The sampling frequency is far lower than the Nyquist sampling frequency, and the signal compression is realized, which greatly saves the sampling resources, transmission bandwidth and storage space. There are three key technologies in compressed sensing: sparse representation, the construction of observation matrix and the design of reconstruction algorithm. The precondition of compression sensing is that the signal is sparse or compressible, while the speech signal is nearly sparse, so the compression perception can be used to process the speech signal. This paper studies the combination of speech and compression perception, and focuses on the design of robust reconstruction algorithm for speech compression perception, because robust reconstruction algorithm is the key to whether compression sensing technology can be applied in practice. The main contents and innovations of this paper are as follows: firstly, the basic theory of compression perception and the combination of speech signal and compression perception are introduced in detail, which verifies the sparsity of speech signal. The performance of the existing representative speech compression sensing observation matrix and reconstruction algorithm is discussed by experimental simulation. Then the effect of noise on speech compression perception is discussed. Secondly, a new fast reconstruction algorithm is studied, which is different from other algorithms. It uses the properties of discrete cosine transform (DCT) and deterministic observation matrix to reduce the complexity of the reconstruction algorithm. However, it is found that the fast reconstruction algorithm is not robust to noise. Therefore, an adaptive fast reconstruction algorithm is proposed, which adaptively selects the optimal reconstruction parameters according to the signal-to-noise ratio of the input speech signal. The experimental results show that the adaptive fast reconstruction algorithm has better anti-noise capability and improves the signal to noise ratio of speech signal reconstruction and the reconstruction speed. Finally, the forward and backward tracking (FBP) algorithm is analyzed, and it is found that the forward step size and the backward step size are fixed, that is, the number of elements added to the support set is fixed during each iteration, which will lead to the unsatisfactory convergence rate of the algorithm. Because in the process of reconstruction, the signal components in the residuals are less and less, so the step size of the iteration should be increased to speed up the reconstruction of the algorithm. Therefore, a fast forward backward tracking (FFBP) algorithm is proposed, which dynamically adjusts the forward step size according to the change rate of the residuals of two adjacent iterations, and finally improves the speed of speech signal reconstruction. Experimental results show that the FFBP algorithm has the same SNR as the FBP algorithm, but the reconstruction speed of the FFBP algorithm is obviously faster than that of the FBP algorithm.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TN912.3

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