Blind separation of audio signals using trigonometric transforms and Kalman filtering

This paper deals with the problem of blind separation of audio signals from noisy mixtures. It proposes the application of a blind separation algorithm on the Discrete Cosine Transform (DCT) or the Discrete Sine Transform (DST) of the mixed signals, instead of performing the separation on the mixtures in the time domain. Kalman Filtering of the noisy separated signals is recommended in this paper as a post-processing step for noise reduction. Both the DCT and the DST have an energy compaction property, which concentrates most of the signal energy in a few coefficients in the transform domain, leaving the rest of the transform-domain coefficients close to zero. As a result, the separation is performed on a few coefficients in the transform domain. Another advantage of signal separation in transform domains is that the effect of noise on the signals in the transform domains is smaller than that in the time domain due to the averaging effect of the transform equations. The simulation results confirm the effectiveness of transform-domain signal separation and the feasibility of the post-processing Kalman filtering step.     

Wavelet domain-based video noise reduction using temporal discrete cosine transform and hierarchically adapted thresholding

A novel spatio-temporal filter for video denoising, which operates entirely in the wavelet domain, is proposed. For effective noise reduction, the spatial and temporal redundancies that exist in the wavelet domain representation of a video signal are exploited. First, a 2D discrete wavelet transform is applied to the input noisy frames. This is followed by a discrete cosine transform (DCT), which is applied to the temporal subband coefficients to minimise the redundancy among the consecutive frames. The DCT transformed, noise-free coefficients in the different wavelet domain subbands for the original image sequence are modelled using a prior having a generalised Gaussian distribution. On the basis of this prior, filtering of the noisy wavelet coefficients in each subband is carried out using a new, low-complexity wavelet shrinkage method, which utilises the correlation that exists between subsequent resolution levels. Experimental results show that the proposed scheme outperforms several state-of-the-art spatio-temporal filters in terms of both the peak signal-to-noise ratio and the visual quality     

复数Curvelet 变换域复数高斯尺度混合图像降噪

提出了一种基于复数Curvelet 变换域复数高斯尺度混合（CGSM）模型的图像去噪方法．指出Curvelet 变换重构图像存在“划痕”和“嵌入污点”的主要原因是Curvelet 变换域存在频谱混叠,为此,采用复数小波变换和 改进的Radon 变换分别代替原Curvelet 变换中的实小波变换和Radon 变换．构造了具有抗混叠性能的复数Curvelet 变换．本文同时把高斯尺度混合（GSM）模型扩展到复小波域,形成对复小波系数的幅值和相位信息具有有效捕捉 能力的复数GSM 模型,并在复数Curvelet 变换域,采用贝叶斯最小平方（BLS）估计器对CGSM 模型下含噪复系数 进行有效估计,从而实现降噪．实验结果表明,无论是用PSNR 指标评估,还是在视觉效果上,本文方法的去噪性能 均好于传统Curvelet 去噪、Curvelet 域HMT 去噪和小波域BLS-GSM 去噪．本文方法在有效去噪的同时,具有很好 的图像边缘和细节保护能力．     

An adaptive edge-preserving image denoising technique using patch-based weighted-SVD filtering in wavelet domain

Image denoising has always been one of the standard problems in image processing and computer vision. It is always recommendable for a denoising method to preserve important image features, such as edges, corners, etc., during its execution. Image denoising methods based on wavelet transforms have been shown their excellence in providing an efficient edge-preserving image denoising, because they provide a suitable basis for separating noisy signal from the image signal. This paper presents a novel edge-preserving image denoising technique based on wavelet transforms. The wavelet domain representation of the noisy image is obtained through its multi-level decomposition into wavelet coefficients by applying a discrete wavelet transform. A patch-based weighted-SVD filtering technique is used to effectively reduce noise while preserving important features of the original image. Experimental results, compared to other approaches, demonstrate that the proposed method achieves very impressive gain in denoising performance.     

A new wavelet-based fuzzy single and multi-channel image denoising

In this paper, we propose a new wavelet shrinkage algorithm based on fuzzy logic. In particular, intra-scale dependency within wavelet coefficients is modeled using a fuzzy feature. This feature space distinguishes between important coefficients, which belong to image discontinuity and noisy coefficients. We use this fuzzy feature for enhancing wavelet coefficients' information in the shrinkage step. Then a fuzzy membership function shrinks wavelet coefficients based on the fuzzy feature. In addition, we extend our noise reduction algorithm for multi-channel images. We use inter-relation between different channels as a fuzzy feature for improving the denoising performance compared to denoising each channel, separately. We examine our image denoising algorithm in the dual-tree discrete wavelet transform, which is the new shiftable and modified version of discrete wavelet transform. Extensive comparisons with the state-of-the-art image denoising algorithm indicate that our image denoising algorithm has a better performance in noise suppression and edge preservation.     

地震信号小波变换的去噪方法

运用模极大值法基本原理进行地震信号去噪研究,进而运用二次小波变换原理通过低层系数处理对常用小波去噪方法进行改进.通过合成不同的染噪地震信号,由一系列仿真实验对模拟地震信号进行不同尺度的小波分解与重构,从而实现最优小波分解尺度上的地震信号噪声去除.与常用的快速傅立叶转换方法比较,仿真结果表明,该小波变换方法能够有效去除地震勘探信号中的噪声,并且针对系数的二次小波变换可以明显改进去噪的效果.     

基于级联离散小波变换的信号去噪方法研究

提出了基于级联离散小波变换的信号去噪方法。该方法通过对带噪信号作一层离散小波变换(DWT)后提取的低频部分和高频部分分别作一层DWT和四层DWT,然后,对低频部分提取的低频成分和高频成分均作三层DWT,接着,对所有分解的小波系数进行阈值处理,最后,完成信号重构。实验结果表明:在同样的小波分解层次下,本方法去噪效果好于DWT法和WPD法。     

基于盲源分离的超声信号去噪的仿真研究

提出一种新的基于盲源分离的超声信号去噪方法.为了验证去噪方法的有效性,应用此方法处理了仿真的超声信号,并与小波去噪的效果进行了比较.实验结果表明:该去噪方法能极大提高超声信号的信噪比,且其效果能与小波去噪方法相媲美,其特点是通过超声信号和噪声信号的盲源分离实现噪声消除.     

An Efficient Remote Sensing Image Denoising Method in Extended Discrete Shearlet Domain

Denoising of images is one of the most basic tasks of image processing. It is a challenging work to design a edge-preserving image denoising scheme. Extended discrete Shearlet transform (extended DST) is an effective multi-scale and multi-direction analysis method, it not only can exactly compute the shearlet coefficients based on a multiresolution analysis, but also can provide nearly optimal approximation for a piecewise smooth function. Based on extended DST, an image denoising using fuzzy support vector machine (FSVM) is proposed. Firstly, the noisy image is decomposed into different subbands of frequency and orientation responses using the extended DST. Secondly, the feature vector for a pixel in a noisy image is formed by the spatial regularity in extended DST domain, and the FSVM model is obtained by training. Then the extended DST detail coefficients are divided into two classes (edge-related coefficients and noise-related ones) by FSVM training model. Finally, the detail subbands of extended DST coefficients are denoised by using the adaptive Bayesian threshold. Extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state-of-the-art denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.     

改进的EMD算法及其在含噪盲扰信分离中的应用

针对经验模态分解(EMD)降噪算法存在因表示噪声的内蕴模态函数(IMF)分量选择不当而引起的降噪性能不稳定的问题,对其进行改进,加入对噪声水平的估计,并将噪声阈值作为分解结束的判决门限,避免了对噪声IMF分量的选择。在此基础上,联合小波变换进行降噪,并应用于含噪盲扰信分离中。仿真表明在一定范围的低信噪比条件下,该算法增强了盲扰信分离的抗噪声性能,可将源信号从染噪的观测信号中有效地分离出来。     

盲小波算法在遥感图像去噪中的应用

根据盲信号分离原理和小波分析,提出了一种遥感图像去噪的盲小波算法,首先将遥感图像的个信号进行同深度小波分解,得到不同信号相应深度的小波系数和尺度系数,然后将小波系数进行软阈值法处理,并进一步对不同信号的同深度的小波系数和尺度系数进行盲分离,并提取与源信号相关的信号,最后通过信号重构估计源信号。这种将小波分析和盲信号分离技术有机结合的方法能够有效的消除遥感图像的噪声。通过对实际遥感图像的处理,并与其他去噪技术相比较,利用盲小波算法得到的结果更为理想。     

Wavelet based speech presence probability estimator for speech enhancement

A reliable speech presence probability (SPP) estimator is important to many frequency domain speech enhancement algorithms. It is known that a good estimate of SPP can be obtained by having a smooth a-posteriori signal to noise ratio (SNR) function, which can be achieved by reducing the noise variance when estimating the speech power spectrum. Recently, the wavelet denoising with multitaper spectrum (MTS) estimation technique was suggested for such purpose. However, traditional approaches directly make use of the wavelet shrinkage denoiser which has not been fully optimized for denoising the MTS of noisy speech signals. In this paper, we firstly propose a two-stage wavelet denoising algorithm for estimating the speech power spectrum. First, we apply the wavelet transform to the periodogram of a noisy speech signal. Using the resulting wavelet coefficients, an oracle is developed to indicate the approximate locations of the noise floor in the periodogram. Second, we make use of the oracle developed in stage 1 to selectively remove the wavelet coefficients of the noise floor in the log MTS of the noisy speech. The wavelet coefficients that remained are then used to reconstruct a denoised MTS and in turn generate a smooth a-posteriori SNR function. To adapt to the enhanced a-posteriori SNR function, we further propose a new method to estimate the generalized likelihood ratio (GLR), which is an essential parameter for SPP estimation. Simulation results show that the new SPP estimator outperforms the traditional approaches and enables an improvement in both the quality and intelligibility of the enhanced speeches.     

A Wavelet Packet Tree Denoising Algorithm for Images of Atomic‐Force Microscopy

A threshold‐free denoising procedure of acquired discrete Atomic‐force microscopy (AFM) signals using the discrete wavelet transform (DWT) method is presented in this article. The integration of a denoising procedure into a control structure is extremely important for each kind of system to be controlled. The detection of unavoidable measurement noise in the acquired data of the AFM signal is done by using orthogonal wavelets (Daubechies and Symmlet) and with different polynomial approximation order for each family. The proposed denoising algorithm, based on the free wavelet toolboxes from the WaveLab 850 library of the Stanford University (USA), compares the usefulness of Daubechies and Symmlet wavelets with different vanishing moments. With the help of a seminorm the noise of a sequence is defined as a coherent and incoherent part of the AFM signal. In the first step of the procedure the algorithm analyzes the frequency subspaces of the wavelet packets tree and searches for small or opposing components in the wavelet domains. In the second step of the procedure the incoherent components in the low‐ and high frequency domains are localized and the incoherent is then removed from the AFM signal. The proposed algorithm structure is used to improve the quality of the AFM signals and it can be easily integrated into the existing AFM control hard‐ and software structures. The effectiveness of the proposed denoising algorithm is validated with real measurements.     

Extended Shearlet HMT Model-Based Image Denoising Using BKF Distribution

Images are often corrupted by noise in the procedures of image acquisition and transmission. It is a challenging work to design an edge-preserving image denoising scheme. Extended discrete Shearlet transform (extended DST) is an effective multi-scale and multi-direction analysis method; it not only can exactly compute the Shearlet coefficients based on a multiresolution analysis, but also can represent images with very few coefficients. In this paper, we propose a new image denoising approach in extended DST domain, which combines hidden Markov tree (HMT) model and Bessel K Form (BKF) distribution. Firstly, the marginal statistics of extended DST coefficients are studied, and their distribution is analytically calculated by modeling extended DST coefficients with BKF probability density function. Then, an extended Shearlet HMT model is established for capturing the intra-scale, inter-scale, and cross-orientation coefficients dependencies. Finally, an image denoising approach based on the extended Shearlet HMT model is presented. Extensive experimental results demonstrate that our extended Shearlet HMT denoising approach can obtain better performances in terms of both subjective and objective evaluations than other state-of-the-art HMT denoising techniques. Especially, the proposed approach can preserve edges very well while removing noise.     

基于改进阈值函数的分数阶小波图像去噪

为了消除噪声对图像的影响并较好地保留图像细节信息,提出一种基于改进阈值函数的分数阶小波图像去噪方法。该方法通过分数阶小波变换将含噪信号进行多尺度分解,采用改进的阈值函数对各层分数阶小波域系数进行处理,对处理后的系数进行重构得到去噪后的信号。仿真实验表明,相比已有的软阈值、硬阈值和均值加权法,本文方法去噪后的图像信噪比较大、均方误差较小,取得了满意的视觉效果,是一种实用的去噪方法。     

Image denoising in extended Shearlet domain using hidden Markov tree models

Denoising of images is one of the most basic tasks of image processing. It is a challenging work to design an edge-preserving image denoising scheme. Extended discrete Shearlet transform (extended DST) is an effective multi-scale and multi-direction analysis method; it not only can exactly compute the Shearlet coefficients based on a multiresolution analysis, but also can provide nearly optimal approximation for a piecewise smooth function. In this paper, a new image denoising approach in extended Shearlet domain using hidden Markov tree (HMT) model is proposed. Firstly, the joint statistics and mutual information of the extended DST coefficients are studied. Then, the extended DST coefficients are modeled using an HMT model with Gaussian mixtures, which can effectively capture the intra-scale and inter-scale dependencies. Finally, the extended Shearlet HMT model is applied to image denoising. Extensive experimental results demonstrate that our extended Shearlet HMT denoising method can obtain better performances in terms of both subjective and objective evaluations than other state-of-the-art HMT denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.     

基于修正维纳滤波的小波包变换图像去噪

图像去噪是图像处理中一个非常重要的环节。为了改善降质图像质量,根据Donoho提出的小波阈值去噪算法,分析了维纳滤波原理,提出了一种基于修正维纳滤波的小波包变换图像去噪方法。利用修正维纳滤波对噪声图像进行处理,用处理后的图像计算噪声的标准方差,以此作为小波包的阈值。利用小波包对维纳滤波后的图像进行分解,实现对图像的低频和高频部分分别进行分解,用计算出的阈值对小波包树系数进行软阈值处理。利用小波包逆变换来获取去噪后的图像。结果表明：在噪声方差为0.01时,经该算法去噪后图像的PSNR比小波包自适应阈值去噪后的PSNR高出8.8 dB。该算法不仅能有效地去除加性高斯白噪声,而且能很好地保留边缘信息,极大地改善了图像的视觉质量。     

基于PCA的图像小波去噪方法

目前使用的各种小波去噪方法基本上都是建立在对噪声方差精确估计的基础上，而对噪声方差的精确估计是很困难的．提出了一种采用主分量分析（PCA）提取小波系数的主要特征，通过对小波域中噪声能量的估计来实现去噪的新方法．首先利用PCA对小波高频子带进行局部特征提取；然后以主分量对小波系数进行重建的平均能量作为局部噪声能量的估计；将原小波系数的能量减去噪声能量，就得到去噪后的小波系数；最后用小波逆变换对剔除噪声分量后的小波系数进行恢复得到去噪后的图像．本文算法无需对噪声方差进行估计，因而更具实用价值．本文算法与“软阈值”、“硬阈值”去噪方法相比，峰值信噪比（PNNR）提高了2～8dB．实验证实了本文算法良好的去噪性能。     

基于改进阈值函数的分数阶小波电能信号去噪

为了消除电力系统中噪声对电能质量扰动信号的影响,且能保留突变点信息,提出了一种基于改进阈值函数的分数阶小波电能质量扰动信号去噪方法.该方法采用离散分数阶小波变换对含噪信号进行多尺度分解,并根据信号和噪声在不同尺度上的分数阶小波域系数的分布特点,通过改进阈值函数对各层系数进行处理,将处理后的系数进行重构得到去噪后的信号.仿真结果表明,该方法弥补了软、硬阈值函数的缺点,能较好地去除噪声并保留突变点信息,且提高了输出信噪比.     

小波分析在微重量动态称重中的应用研究

论述了小波分析在微重量动态称重信号降噪中的应用。主要分析如何引入小波变换理论,并通过小波去除微重量动态称重信号中的噪声。阐述了小波分析去噪及其相对FFT除噪方法的优势。结果表明,用小波变换处理含噪信号,具有明显效果。