基于压缩感知的二维DOA估计

针对L阵列,提出基于压缩感知的二维波达方向估计新方法。定义方位角和俯仰角余弦乘积为空间合成角,利用等余弦网格划分空间合成角构造超完备的冗余字典,将子阵接收的单快拍数据矢量转化为冗余字典下的稀疏表示问题;采用单位列向量组合矩阵随机抽取的新方法构造高斯随机测量矩阵;通过改进正交匹配追踪算法求解二维波达角。指出所提出的算法比传统二维MUSIC算法在高信噪比、多快拍条件下估计性能更好,并且有一定的阵元节约效能。计算机仿真实验证明了以上结论。     

2D sparse signal recovery via 2D orthogonal matching pursuit

Recovery algorithms play a key role in compressive sampling (CS).Most of current CS recovery algo-rithms are originally designed for one-dimensional (1D) signal,while many practical signals are two-dimensional (2D).By utilizing 2D separable sampling,2D signal recovery problem can be converted into 1D signal recovery problem so that ordinary 1D recovery algorithms,e.g.orthogonal matching pursuit (OMP),can be applied directly.However,even with 2D separable sampling,the memory usage and complexity at the decoder are still high.This paper develops a novel recovery algorithm called 2D-OMP,which is an extension of 1D-OMP.In the 2D-OMP,each atom in the dictionary is a matrix.At each iteration,the decoder projects the sample matrix onto 2D atoms to select the best matched atom,and then renews the weights for all the already selected atoms via the least squares.We show that 2D-OMP is in fact equivalent to 1D-OMP,but it reduces recovery complexity and memory usage significantly.What’s more important,by utilizing the same methodology used in this paper,one can even obtain higher dimensional OMP (say 3D-OMP,etc.) with ease.     

基于小波变换和K-SVD的应急广播语音压缩方法

针对应急广播中语音传输效率低的问题,提出了一种基于小波变换和K-奇异值分解（K-SVD）的语音压缩方法,以提升应急广播的信息传输时效性。首先,该方法舍弃语音小波分解得到的高频分量,在小波合成时用随机信号代替;其次,在低频分量的压缩感知过程中,用K-SVD字典学习算法训练的过完备字典对其稀疏表示;最后,采用改进的基于子空间回溯的广义正交匹配追踪算法重构信号。实验结果表明,在压缩效率为50%时,该方法重构应急广播语音的客观语音质量评分（PESQ）达到3.717,比其他对照算法分别提升了3%~47%,说明在保证压缩效率的同时,所提出的方法能提升应急广播语音重构质量,确保应急广播的传输时效性。     

Blind source separation by sparse decomposition in a signal dictionary

The blind source separation problem is to extract the underlying source signals from a set of linear mixtures, where the mixing matrix is unknown. This situation is common in acoustics, radio, medical signal and image processing, hyperspectral imaging, and other areas. We suggest a two-stage separation process: a priori selection of a possibly overcomplete signal dictionary (for instance, a wavelet frame or a learned dictionary) in which the sources are assumed to be sparsely representable, followed by unmixing the sources by exploiting the their sparse representability. We consider the general case of more sources than mixtures, but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures. Experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques.     

不同特征数字信号的谱估计算法性能分析

通过实验八种经典和现代的数字信号谱估计算法,并分析了这几种谱估计算法对不同特性信号主要包括周期信号、声音信号和随机信号的影响和差异,从这些算法所表现出的特征和差异中得出针对不同特征信号的谱估计算法性能的优劣性.     

Denoising for Multiple Image Copies through Joint Sparse Representation

This paper addresses the recovery of original images from multiple copies corrupted with the noises, which can be represented sparsely in some dictionary. Sparse representation has been proven to have strong ability to denoise. However, it performs suboptimally when the noise is sparse in some dictionary. A novel joint sparse representation (JSR)-based image denoising method is proposed. The images can be recovered well from multiple noisy copies. All copies share a common component—the image, while each individual measurement contains an innovation component—the noise. Our method can separate the common and innovation components, and reconstruct the images with the sparse coefficients and the dictionaries. Experiment results show that the performance of the proposed method is better than that of other methods in terms of the metric and the visual quality.     

Maximum contrast analysis for nonnegative blind source separation

In this paper, we propose a maximum contrast analysis (MCA) method for nonnegative blind source separation, where both the mixing matrix and the source signals are nonnegative. We first show that the contrast degree of the source signals is greater than that of the mixed signals. Motivated by this observation, we propose an MCA-based cost function. It is further shown that the separation matrix can be obtained by maximizing the proposed cost function. Then we derive an iterative determinant maximization algorithm for estimating the separation matrix. In the case of two sources, a closed-form solution exists and is derived. Unlike most existing blind source separation methods, the proposed MCA method needs neither the independence assumption, nor the sparseness requirement of the sources. The effectiveness of the new method is illustrated by experiments using X-ray images, remote sensing images, infrared spectral images, and real-world fluorescence microscopy images.     

基于准正交原理的多信源少观测源的盲语音信号分离

信号源个数多于观测信号个数情况下的盲源分离问题是盲信号分离中的一个难题,也是一个很实际的问题。论文在A.Hyvrinen提出的一种基于准正交原理的盲分离算法基础上,指出当混合矩阵的基矢量不满足准正交性时,可以对观测信号预白化,使混合矩阵的基矢量的准正交性得以很大提高。然后将此方法用于多信源少观测源情况下的混合语音信号分离。实验分为两个过程:(1)估计混合矩阵;(2)用最大后验概率的估计方法分离源语音信号。实验结果证明了该算法能够有效用于高维情况下多信源少观测源的盲语音信号分离。     

过完备ICA 算法在语音信号提取中的应用

在语音信号处理中常用麦克风采集语音,然后用算法进行提取和分离,目前常用的有独立分量分析（Independent component Analysis,ICA）算法。但是当麦克风个数少于说话人的个数时,即欠定情形,此时语音信号的提取需采用过完备ICA算法。提出了一种基于过完备ICA算法的两步算法：估计混合矩阵的几何算法和估计源矩阵的最短路径法。该算法能在欠定情形下对语音信号的提取有很好的作用,仿真实验验证了这一结果。     

基于稀疏表示和约束优化的波达方向估计方法

对于噪声环境中信号源的波达方向(DOA)估计,传统的多信号分类(MUSIC)算法只对不相干信号有效,且所需较多样本。针对此问题,将进行DOA估计的搜索范围看作冗余字典,从而待估计的DOA成为该冗余字典中的某些元素,可以由冗余字典对其进行稀疏表示;其次,利用单次快拍数据,应用二阶锥(SOC)约束优化的方法对该稀疏表示问题进行描述,并进而转化为标准的二阶锥形式,采用有效的优化工具SeDuMi来实现DOA的估计。仿真结果表明,与现有的子空间方法相比,该方法只需单拍数据即可得到较好的估计结果,且无需对信源个数有先验知识,同时适用于相干和非相干信号。     

Independent Component Analysis for Time-dependent Processes Using AR Source Model

Independent component analysis is a fundamental and important task in unsupervised learning, that was studied mainly in the domain of Hebbian learning. In this paper, the temporal dependencies are explained by assuming that each source is an autoregressive (AR) process and innovations are independently and identically distributed (i.i.d). First, the likelihood of the model is derived, which takes into account both spatial and temporal information of the sources. Next, batch and on-line blind source separation algorithms are developed by maximizing likelihood function, and their local stability analysis are introduced simultaneously. Finally, computer simulations show that the algorithms achieve better separation of the mixed signals and mixed nature images which are difficult to be separated by the basic independent component analysis algorithms.     

Convergence analysis of the OJAn MCA learning algorithm by the deterministic discrete time method

Minor component analysis (MCA) is a statistical method of extracting the eigenvector associated with the smallest eigenvalue of the covariance matrix of input signals. Convergence is essential for MCA algorithms towards practical applications. Traditionally, the convergence of MCA algorithms is indirectly analyzed via their corresponding deterministic continuous time (DCT) systems. However, the DCT method requires the learning rate to approach zero, which is not reasonable in many applications due to the round-off limitation and tracking requirements. This paper studies the convergence of the deterministic discrete time (DDT) system associated with the OJAn MCA learning algorithm. Unlike the DCT method, the DDT method does not require the learning rate to approach zero. In this paper, some important convergence results are obtained for the OJAn MCA learning algorithm via the DDT method. Simulations are carried out to illustrate the theoretical results achieved.     

On MAP and MMSE estimators for the co-sparse analysis model

The sparse synthesis model for signals has become very popular in the last decade, leading to improved performance in many signal processing applications. This model assumes that a signal may be described as a linear combination of few columns (atoms) of a given synthesis matrix (dictionary). The Co-Sparse Analysis model is a recently introduced counterpart, whereby signals are assumed to be orthogonal to many rows of a given analysis dictionary. These rows are called the co-support.The Analysis model has already led to a series of contributions that address the pursuit problem: identifying the co-support of a corrupted signal in order to restore it. While all the existing work adopts a deterministic point of view towards the design of such pursuit algorithms, this paper introduces a Bayesian estimation point of view, starting with a random generative model for the co-sparse analysis signals. This is followed by a derivation of Oracle, Minimum-Mean-Squared-Error (MMSE), and Maximum-A-posteriori-Probability (MAP) based estimators. We present a comparison between the deterministic formulations and these estimators, drawing some connections between the two. We develop practical approximations to the MAP and MMSE estimators, and demonstrate the proposed reconstruction algorithms in several synthetic and real image experiments, showing their potential and applicability.     

A class of learning algorithms for principal component analysis andminor component analysis

Principal component analysis (PCA) and minor component analysis (MCA) are a powerful methodology for a wide variety of applications such as pattern recognition and signal processing. In this paper, we first propose a differential equation for the generalized eigenvalue problem. We prove that the stable points of this differential equation are the eigenvectors corresponding to the largest eigenvalue. Based on this generalized differential equation, a class of PCA and MCA learning algorithms can be obtained. We demonstrate that many existing PCA and MCA learning algorithms are special cases of this class, and this class includes some new and simpler MCA learning algorithms. Our results show that all the learning algorithms of this class have the same order of convergence speed, and they are robust to implementation error.     

连续波背景下多信号处理方法

对接收到的信号进行短时傅里叶变换，通过分析短时傅里叶变换中每一个时间片内的信号频谱，检测出连续波背景下的脉冲信号。滤除线性调频脉冲信号成分，保留连续波信号成分，得到调频连续波信号具有周期性的时频变化曲线。根据连续波信号时频变化曲线的频谱特征，估计出其主要参数，然后滤除脉冲信号出现时间内信号中的连续波成分，并采用相应的方法估计出其参数。仿真结果表明，本文算法可以准确估计出线性调频连续波（LFMCW）信号和线性调频（LFM）脉冲信号的参数，当LFMCW信号的信噪比高于-8dB，并且其功率比脉冲信号功率小6dB以上时，算法具有良好的估计精度和稳定性。     

基于ICA的周期性噪声消除算法

为了使问题有解，传统的独立分量分析算法对问题的条件有许多严格的限制，其中包括观测信号的个数不能小于源信号的个数等．在降噪等实际应用中，观测信号的个数可能无法满足这一条件，为了能够利用独立分量分析分离加性噪声，需要人工构造混合信号．基于周期性干扰表现的整体周期性，提出了一种构造混合信号的新算法．利用构造的混合信号进行独立分量分析，可以有效地消除周期性干扰，使目标信号的信噪比显著提高．即使在信噪比很低，目标信号几近被“淹没”的情况下，仍然能够较好地将其分离出来．该方法具有算法简单、运算速度快、算法效率高等特点．计算机仿真和实验结果都证明了算法的有效性．     

基于Pearson系统模型的盲信号分离研究

独立分量分析是盲源分离的主流技术.自然梯度算法是其中非常重要的算法之一.介绍一种最大似然框架下的Pearson系统模型.该方法的优点是无须知晓信号的概率分布,实验结果表明,该算法能有效地分离随机混合的信号,特别对于非对称源有比同类算法更理想的效果.     

联合过完备库下的信号稀疏分解

针对具有多个特征成分的复合信号在单一特征过完备库下无法实现稀疏分解的问题,提出构建联合过完备库的思想.联合过完备库由多个具有单一特征的过完备库联合构成,包含复合信号中各分量信号的信息,使得复合信号在其上具有稀疏性.利用稀疏分解算法,对多个复合信号在相应的联合过完备库上进行稀疏分解和信号重构,并与单一特征过完备库的分解结果进行了对比分析.仿真结果表明了构建联合过完备库思想的合理性和有效性.     

基于形态学成分分析的指纹分离

针对指纹图像的特点,对形态学成分分析进行改造,将其与角点检测器相结合,提出了一种指纹分离算法。算法基于基追踪去噪算法,首先对重叠指纹图像或者指纹与背景纹理重叠的图像采用两个相同的纹理词典进行稀疏表示,对稀疏系数软门限收缩之后进行反变换得到两幅纹理图像,然后使用梯度下降法最小化分离出来的两幅纹理图像的harris-like算子,使得两幅图像的角点均最少,再对其中一幅图像进行全方差调整,从而达到分离的目的。实验结果表明此方法能够实现指纹分离。