Wavelet denoising via sparse representation

Wavelet threshold denoising is a powerful method for suppressing noise in signals and images. However, this method often uses a coordinate-wise processing scheme, which ignores the structural properties in the wavelet coefficients. We propose a new wavelet denoising method using sparse representation which is a powerful mathematical tool recently developed. Instead of thresholding wavelet coefficients individually, we minimize the number of non-zero coefficients under certain conditions. The denoised signal is reconstructed by solving an optimization problem. It is shown that the solution to the optimization problem can be obtained uniquely and the estimates of the denoised wavelet coefficients are unbiased, i.e., the statistical means of the estimates are equal to the noise-free wavelet coefficients. It is also shown that at least a local optimal solution to the denoising problem can be found. Our experiments on test data indicate that this new denoising method is effective and efficient for a wide variety of signals including those with low signal-to-noise ratios. Supported by the U.S. National Institutes of Health (Grant No. U01 HL91736), and the National High-Tech Research & Development Program of China (Grant No. 2007AA01Z175)     

Adaptive Denoising Using a Modified Sparse Coding Shrinkage Method

This paper proposes a novel denoising method for natural images by using a modified sparse coding (SC) algorithm, which is self-adaptive to the statistical property of natural images. The main idea is to utilize the shrinkage function, which is selected according to the prior distribution of sparse components, to the sparse components to remove Gaussian white noise added in an image. This denoising method is respectively evaluated by the criteria of normalized mean squared error (NMSE), Laplace mean square error (LMSE) and peak signal to noise ratio (PSNR). Compared with other denoising methods, the simulation results show that our sparse coding shrinkage technique is indeed effective and efficient.     

多媒体信号处理的数学理论前沿进展

深度学习模型广泛应用于多媒体信号处理领域,通过引入非线性能够极大地提升性能,但是其黑箱结构无法解析地给出最优点和优化条件。因此如何利用传统信号处理理论,基于变换/基映射模型逼近深度学习模型,解析优化问题,成为当前研究的前沿问题。本文从信号处理的基础理论出发,分析了当前针对高维非线性非规则结构方法的数学模型和理论边界,主要包括：结构化稀疏表示模型、基于框架理论的深度网络模型、多层卷积稀疏编码模型以及图信号处理理论。详细描述了基于组稀疏性和层次化稀疏性的表示模型和优化方法,分析基于半离散框架和卷积稀疏编码构建深度/多层网络模型,进一步在非欧氏空间上扩展形成图信号处理模型,并对国内外关于记忆网络的研究进展进行了比较。最后,展望了多媒体信号处理的理论模型发展,认为图信号处理通过解析谱图模型的数学性质,解释其中的关联性,为建立广义的大规模非规则多媒体信号处理模型提供理论基础,是未来研究的重要领域之一。     

FFT和小波变换在信号降噪中的应用

信号降噪是指滤除信号的高频噪声从而使信号尽量接近真实值,这是信号处理的关键环节.在分析FFT和小波变换的基础上,采用这两种方法对加入随机噪声的信号进行降噪处理,并在MATLAB平台上仿真实现.用基于信号降噪的两大准则对两种降噪结果进行分析,表明小波变换在该信号的降噪处理中有明显的优势.     

二阶收敛的光滑正则化压缩感知信号重构方法

目的压缩感知信号重构过程是求解不定线性系统稀疏解的过程。针对不定线性系统稀疏解3种求解方法不够鲁棒的问题:最小化l₀-范数属于NP问题,最小化l₁-范数的无解情况以及最小化l_p-范数的非凸问题,提出一种基于光滑正则凸优化的方法进行求解。方法为了获得全局最优解并保证算法的鲁棒性,首先,设计了全空间信号l₀-范数凸拟合函数作为优化的目标函数;其次,将n元函数优化问题转变为n个一元函数优化问题;最后,求解过程中利用快速收缩算法进行求解,使收敛速度达到二阶收敛。结果该算法无论在仿真数据集还是在真实数据集上,都取得了优于其他3种类型算法的效果。在仿真实验中,当信号维数大于150维时,该方法重构时间为其他算法的50%左右,具有快速性;在真实数据实验中,该方法重构出的信号与原始信号差的F-范数为其他算法的70%,具有良好的鲁棒性。结论本文算法为二阶收敛的凸优化算法,可确保快速收敛到全局最优解,适合处理大型数据,在信息检索、字典学习和图像压缩等领域具有较大的潜在应用价值。     

A pulsed neural network model of spectro-temporal receptive fields and population coding in auditory cortex

The existence of spectro-temporal receptive fields and evidence for population coding in auditory cortex motivate the development of such models, that explicitly operate in the time-frequency domain and are based on a pulsed neural network. In presenting such a model, a formal connection of the fields of Time Frequency Analysis and Pulsed Neural Networks is established. The resulting neural time-frequency signal representation is shown to be representable as a signal-dependent overcomplete dictionary. It is derived from neural population coding. Signal decomposition and filtering effects are presented, indicating obvious technical applications of the proposed model. This revised version was published online in June 2006 with corrections to the Cover Date.     

LWT-FLP去噪算法在FBG传感器信号处理中的应用

为了提高传感器信号处理的精度,结合提升小波变换和前向线性预测算法的优势,提出了一种新的去噪LWT-FLP去噪算法,首先利用提升小波对加速度计数据进行了多尺度变换,降低了原始数据的不平稳性;其次利用高频数据进行灰化处理,使原本无规律的数据体现出一定的规律性,可以有效提高FLP的预测精度。并对FBG传感器信号进行应用结果表明,提出的算法能够有效去除噪声对FBG传感器输出信号的影响,有效地证明了提出的LWT-FLP算法在去噪方面的优越性。通过与单一的算法进行去噪结果对比,验证了该算法的准确性,为传感器信号处理提供了一定的理论新方法。     

Searching-and-averaging method of underdetermined blind speech signal separation in time domain

Underdetermined blind signal separation (BSS) (with fewer observed mixtures than sources) is discussed. A novel searching-and-averaging method in time domain (SAMTD) is proposed. It can solve a kind of problems that are very hard to solve by using sparse representation in frequency domain. Bypassing the disadvantages of traditional clustering (e.g., K-means or potential-function clustering), the durative- sparsity of a speech signal in time domain is used. To recover the mixing matrix, our method deletes those samples, which are not in the same or inverse direction of the basis vectors. To recover the sources, an improved geometric approach to overcomplete ICA (Independent Component Analysis) is presented. Several speech signal experiments demonstrate the good performance of the proposed method.     

Image restoration approach using a joint sparse representation in 3D-transform domain

Image restoration is a crucial problem in image processing and a necessary step before the image segmentation and recognition. A new framework for image restoration in 3D transform domain terms as joint sparse representation (JSR) is proposed in this work. The proposed JSR is able to represent image more sparsely and more precisely in the transform domain by performing 3D transform on each set of similar blocks. In addition to that, in order to overcome the issues of defective block matching and spurious artifact in the 3D sparse representation, JSR introduces a new nonlocal regularization term which characterizes the statistics of the nonlocal image to improve the accuracy of the estimated coefficients. The parameters of regularization terms are calculated based on Bayesian philosophy, and a split Bregman-based technique is developed to obtain the solution in a tractable and robust manner. Extensive experiments on image denoising, image inpainting and image deblurring demonstrate that the proposed JSR algorithm outperforms current state-of-the-art approaches in terms of peak signal-to-noise ratio and visual quality.     

Finding independent components using spikes: A natural result of hebbian learning in a sparse spike coding scheme

As an alternative to classical representations in machine learning algorithms, we explore coding strategies using events as is observed for spiking neurons in the central nervous system. Focusing on visual processing, we have previously shown that we can define with an over-complete dictionary a sparse spike coding scheme by implementing lateral interactions that account for redundant information. Since this class of algorithms is both compatible with biological constraints and with neuro-physiological observations, it can provide a possible algorithm to explain the speed of visual processing despite the relatively slow time of response of single neurons. Here, I explore learning mechanisms to derive in an unsupervised manner an over-complete set of filters which provides a progressively sparser representation of the input. This work is based on a previous model of sparse coding from Olshausen et al. (1998) and the results leads to similar results, suggesting that this strategy provides a simple neural implementation of this algorithm and thus of Blind Source Separation. Moreover, this neuro-mimetic algorithm may be easily extended to realistic architectures of cortical columns in the primary visual cortex and we show results for different strategies of representation, leading to neuro-mimetic adaptive sparse spike coding schemes. This revised version was published online in June 2006 with corrections to the Cover Date.