基于主分量分析的语音信号压缩感知

压缩感知理论是近年来兴起的一个新的研究热点。寻求适合于语音信号的稀疏基是压缩感知理论应用到语音信号处理领域的前提。本文基于主分量分析理论和大量的块数据,提取语音信号的特征信息,并根据压缩感知理论、字典构造的方法以及语音信号的特点,构造出一种新的适合于语音信号稀疏表示的冗余字典。该冗余字典是由多个正交基级联而成。为了更为客观的说明这种稀疏表示的优势,采用两种稀疏度的衡量标准来分别比较语音信号在DCT基、GABOR基和该冗余字典下的稀疏性,并且分别对男女声语音信号和清浊音进行了分析。实验表明,无论是男声信号还是女声信号,清音还是浊音,在该冗余字典下的稀疏性均优于DCT基,略差于GABOR基,但是由于其原子数远少于GABOR基,其计算的复杂度和存储量均低于GABOR基,因而比GABOR基更具可用性。      

压缩感知的冗余字典及其迭代软阈值实现算法

冗余字典的信号稀疏分解是一种新的信号表示理论,采用超完备的冗余函数系统代替传统的正交基函数,为信号自适应地稀疏扩展提供了极大的灵活性。本文研究了压缩感知理论下的冗余字典、测量矩阵及其限制等容特性(RIP,Restricted Isometry Property),并给出了RIP、字典大小、稀疏度和测量次数的关系,提出了一种新的迭代软阈值(IST)算法,与正交匹配追踪(OMP)算法和迭代硬阈值(IHT)算法相比较,实验结果表明了IST算法具有更高的信号恢复率。     

冗余字典在压缩感知中的应用研究

信号的稀疏表示是压缩感知理论中的关键问题,一般选择正交基作为压缩感知中的稀疏变换基。因为冗余字典能更有效的表示信号的特征,使得信号能用字典中的少量原子线性表示,因此本文对冗余字典在压缩感知理论中的应用进行了研究。设计了由不同正交基与单位矩阵组成的3种简洁冗余字典,作为压缩感知的稀疏变换基。以一维信号作为测试信号,研究了冗余字典的稀疏表示和算法重构的性能。实验结果证明了冗余字典在压缩感知理论中应用的有效性。     

利用稳健字典学习的雷达高分辨距离像目标识别算法

基于字典学习算法的信号稀疏表示被广泛应用于信号处理领域。由于字典原子间存在冗余性,求解信号的稀疏表示会受到观测信号中扰动分量的影响,从而带来表示的不确定性,不利于雷达高分辨距离像(HRRP)目标识别任务。针对这一问题,该文提出一种稳健字典学习(SDL)算法,通过边缘化信号丢失,构建稳健损失函数用于学习自适应字典。该算法利用距离像在散射点不发生越距离单元走动的方位帧内具有结构相似性,约束临近训练样本间稀疏表示的非零元素位置相同,并通过结构化稀疏约束选择最优子字典用于测试样本的分类。基于实测HRRP数据的实验结果验证了所提算法的有效性。     

基于自适应稀疏表示的电子商务语音识别增强方法研究

传统语音增强算法在去除噪声的同时也导致语音受损，为了减小这种负面影响，结合了语音信号的稀疏表示算法与语音增强算法和自适应的获得训练字典，提出了一种基于自适应稀疏表示的语音增强算法。仿真实验结果表明该方法即使在低信噪比的条件下也能有效去噪，且去噪后能很好的分辨出原始语音信号。     

基于数据驱动字典和稀疏表示的语音增强

本文提出了一种基于数据驱动字典和过完备稀疏表示的自适应语音增强方法。首先在训练阶段采用干净语音基于K奇异值分解(K singular value decomposition, K SVD)算法训练过完备字典,然后在测试阶段根据含噪语音的噪声方差自适应选择最优的阈值,采用正交匹配追踪算法对含噪语音信号在过完备字典上进行稀疏分解,最后利用系数稀疏表示重构语音信号,从而达到语音增强的目。该方法不像传统语音增强方法那样减少或消去噪声,而是从字典中选取适当的原子表示纯净信号,从而把纯净信号从含噪信号中分离出来。对白噪声和有色噪声环境下重构语音进行了主客观评价。仿真结果显示:该方法能有效去除加性噪声,并且改善了语音质量。      

非相干子字典多原子快速匹配追踪算法

从冗余字典中得到信号的最稀疏表示是一个NP难问题,即使是次优的匹配追踪仍然相当复杂.该文提出一种多原子快速匹配追踪算法.该算法首先将冗余字典分解成M个非相干的子字典,每次迭代分别从各子字典中至多选取一个满足条件的原子组成多原子集;最后通过求信号在多原子集上的正交投影,得到信号的多原子稀疏逼近.实验采用真实音频信号进行仿真;结果表明新的算法获得与匹配追踪相当的稀疏逼近性能,同时大大提高了信号稀疏分解的速度.     

基于子空间的三阶多项式相位信号快速稀疏分解算法

针对稀疏分解冗余字典中原子数量庞大的缺点,该文提出一种三阶多项式相位信号的快速稀疏分解算法。该算法根据三阶多项式相位信号的特点,把原有信号变换成两个子空间信号,并根据这两个子空间信号构建相应的冗余字典,然后采用正交匹配追踪法来完成其稀疏分解,最后利用稀疏分解原理完成原有信号的稀疏分解。该算法把原有信号变换成两个不同子空间信号,构建了两个不同的冗余字典,对比采用一个冗余字典库,这种采用两个冗余字典的算法大大减少了原子数量,并且通过快速傅里叶变换,在一个冗余字典进行稀疏分解时,同时找到另一个冗余字典中的最匹配的原子。因此该算法通过减少原子数量和采用快速傅里叶变换大大加快了稀疏分解速度。实验结果表明,相比于采用Gabor原子构建的冗余字典,采用匹配追踪算法与遗传算法及最近提出的基于调制相关划分的快速稀疏分解,它的稀疏分解速度更快,并且具有更好的收敛性。     

图约束字典和加权稀疏表示人脸超分辨率算法北大核心

针对低分辨率、低质量人脸图像重建问题,提出了一种新的基于稀疏表示的人脸超分辨率算法。在训练阶段,人脸的位置特征被用于保持人脸块的全局信息,人脸块间的几何结构被用于保持高低分辨率超完备冗余字典的流形结构,从而提高字典的表达能力;在重建阶段,K近邻加权稀疏表示被用于消除稀疏编码噪声,以提高高分辨率人脸图像重建系数的精度。实验结果表明,提出的方法取得了较好的主客观质量。     

基于块分类稀疏表示的图像融合算法

针对基于单一字典训练稀疏表示的图像融合算法忽略图像局部特征的问题,提出了基于块分类稀疏表示的图像融合算法。此算法是根据图像局部特征的差异将图像块分为平滑、边缘和纹理三种结构类型,对边缘和纹理结构分别训练出各自的冗余字典。平滑结构利用算术平均法进行融合,边缘和纹理结构由对应字典利用稀疏表示算法进行融合,并对边缘结构稀疏表示中的残余量进行小波变换融合。实验结果证明,该算法相对于单一字典稀疏表示算法,在融合图像的主观评价和客观评价指标上都有显著改进,并且算法速度也有提高。     

Compression of facial images using the K-SVD algorithm

The use of sparse representations in signal and image processing is gradually increasing in the past several years. Obtaining an overcomplete dictionary from a set of signals allows us to represent them as a sparse linear combination of dictionary atoms. Pursuit algorithms are then used for signal decomposition. A recent work introduced the K-SVD algorithm, which is a novel method for training overcomplete dictionaries that lead to sparse signal representation. In this work we propose a new method for compressing facial images, based on the K-SVD algorithm. We train K-SVD dictionaries for predefined image patches, and compress each new image according to these dictionaries. The encoding is based on sparse coding of each image patch using the relevant trained dictionary, and the decoding is a simple reconstruction of the patches by linear combination of atoms. An essential pre-process stage for this method is an image alignment procedure, where several facial features are detected and geometrically warped into a canonical spatial location. We present this new method, analyze its results and compare it to several competing compression techniques.     

组合正交基字典稀疏分解快速匹配追踪算法

组合正交基字典稀疏分解通过正交基的级联来构造完备字典,实现稀疏分解。针对稀疏分解的常见算法计算复杂度高的问题,提出一种快速匹配追踪算法。该算法首先求出并存储正交基向量之间的内积,然后根据向量正交基展开系数为其与正交基向量内积的性质将内积运算转化为代数运算,得到一种快速匹配追踪算法。实验结果表明,基于Dirac基和DCT基构成的完备字典对信号leleccum进行稀疏分解时,与匹配追踪(MP)算法相比,该算法的计算速度提高了大约10倍。     

基于稀疏表达的图像去噪方法研究

提出一种基于混合字典的图像稀疏分解去噪方法。使用小波包函数和离散余弦函数构成混合字典,采用匹配追踪算法对图像进行稀疏分解,提取含噪图像中的稀疏成分,最后利用稀疏成分进行图像重构,达到去除图像中噪声的目的。实验中与单一字典稀疏分解去噪算法进行了对比,结果表明,所提出的混合字典稀疏去噪算法可有效提取图像中的稀疏结构,改善重构图像的主客观质量。     

一种基于匹配追踪的语音盲源分离算法

研究基于Gabor的过完备字典的匹配追踪（Matching Pursuit,MP）稀疏分解算法,首先对混合语音信号进行稀疏分解。针对传统MP算法运行时间长,占用存储范围大以及语音信号稀疏分解特性的特点,利用快速傅里叶变换（Fast Fourier Transformation,FFT）的MP稀疏分解缩小了最佳原子的搜索范围,提高运行速度。然后基于峭度的自适应盲源分离算法,通过自适应地学习算法中的激活函数最终实现语音信号的盲源分离。此算法经过仿真实验,证明分离效果比传统算法有了一定的改进,实验结果证实算法的有效性。     

基于迭代自适应稀疏分解的雷达信号去噪

稀疏分解能有效分离信号和噪声,因此适用于信号去噪.文中构造了雷达回波稀疏表示的冗余字典,字典原子与目标回波波形匹配,基于该字典的雷达回波信号稀疏度就是目标数.针对稀疏度自适应匹配追踪算法进行低信噪比信号稀疏分解时的不足,提出了一种迭代自适应匹配追踪算法,采用规范化的残差之差作为迭代终止条件,使得稀疏分解过程能依据噪声水平自适应终止,以逐次逼近方式估计信号稀疏度,改善了稀疏分解的精度.仿真实验结果表明,该算法在低信噪比以及稀疏度未知的条件下,实现了雷达回波信号的准确稀疏分解,极大地提高了信噪比.     

The nonparametric Bayesian dictionary learning based interpolation method for WSNs missing data

The conventional data interpolation methods based on sparse representation usually assume that the signal is sparse under the overcomplete dictionary. Specially, they must confirm the dimensions of dictionary and the signal sparse level in advance. However, it is hard to know them if the signal is complicated or dynamically changing. In this paper, we proposed a nonparametric Bayesian dictionary learning based interpolation method for WSNs missing data, which is the combination of sparse representation and data interpolation. This method need not preset sparse degrees and dictionary dimensions, and our dictionary atoms are drawn from a multivariate normal distribution. In this case, the dictionary size will be learned adaptively by the nonparametric Bayesian method. In addition, we implement the Dirichlet process to exploit the spatial similarity of the sensing data in WSNs, thus to improve the interpolation accuracy. The interpolation model parameters, the optimal dictionary and sparse coefficients, can be inferred by the means of Gibbs sampling. The missing data will be estimated commendably through the derived parameters. The experimental results show that the data interpolation method we proposed outperforms the conventional methods in terms of interpolation accuracy and robustness.     

An image denoising algorithm for mixed noise combining nonlocal means filter and sparse representation technique

Nonlocal means (NLM) filtering or sparse representation based denoising method has obtained a remarkable denoising performance. In order to integrate the advantages of two methods into a unified framework, we propose an image denoising algorithm through skillfully combining NLM and sparse representation technique to remove Gaussian noise mixed with random-valued impulse noise. In the non-Gaussian circumstance, we propose a customized blockwise NLM (CBNLM) filter to generate an initial denoised image. Based on it, we classify the different noisy pixels according to the three-sigma rule. Besides, an overcomplete dictionary is trained on the initial denoised image. Then, a complementary sparse coding technique is used to find the sparse vector for each input noisy patch over the overcomplete dictionary. Through solving a more reasonable variational denoising model, we can reconstruct the clean image. Experimental results verify that our proposed algorithm can obtain the best denoising performance, compared with some typical methods.     

A Criterion for the Construction of a Regularization Function in Sparse Component Analysis

With the application of regularization, sparse component analysis (SCA) becomes an effective approximate method for finding the sparsest solution of signal decomposition in an overcomplete dictionary. In this paper, the authors present some conditions on a family of regularization functions indexed by a hyperparameter so that these functions are applicable and can be effectively optimized in SCA. For a given signal, with these conditions it is proven that there exists at least one hyperparameter such that the global minimum of the corresponding regularization function can theoretically lead to the sparsest representation of the signal. Based on these propositions, a general principle is presented for the construction of regularization functions, and several kinds of function families are recommended for the purpose of sparse signal representation. The paper gives a numerical example that indicates that, for a synthesized signal, minimizing the regularization function proposed in this paper provides the correct sparse solution, whereas the method of basis pursuit fails.