Microarray image enhancement by denoising using decimated and undecimated multiwavelet transforms

In this paper, we present a new approach to deal with the noise inherent in the microarray image processing procedure. We use the denoising capabilities of decimated and undecimated multiwavelet transforms, DMWT and UMWT respectively, for the removal of noise from microarray data. Multiwavelet transforms, with appropriate initialization, provide sparser representation of signals than wavelet transforms so that their difference from noise can be clearly identified. Also, the redundancy of the UMWT transform is particularly useful in image denoising in order to capture the salient features such as noise or transients. We compare this method with the discrete and stationary wavelet transforms, denoted by DWT and SWT, respectively, and the Wiener filter for denoising microarray images. Results show enhanced image quality using the proposed approach, especially in the undecimated case in which the results are comparable and often outperform that of the stationary wavelet transform. Both multiwavelet transforms outperform the DWT and the Wiener filter.     

Image denoising algorithm based on even step-length generalized cross validation model

Generalized cross validation (GCV) is a significant mean square error (MSE) estimator. It is widely used for image denoising because it can provide an optimal denoising threshold for these wavelet coefficients of noise image. However, the computational complexity of GCV is higher than that of the universal threshold denoising algorithm. In this study, an efficient and fast image denoising algorithm is proposed based on even step-length (ESL) GCV model. In ESL-GCV model, only the thresholds on even points are calculated from four to the maximum wavelet coefficient. In addition, the ESL-GCV model is optimized using the integer wavelet transform (IWT). These experimental results show that the IWT-based ESL-GCV model can provide lower computational complexity and the better peak signal-to-noise ratio (PSNR) than those of the traditional GCV. The proposed algorithm has important theoretical and practical value for image denoising in the future.     

Image Denoising Using Trivariate Shrinkage Filter in the Wavelet Domain and Joint Bilateral Filter in the Spatial Domain

This correspondence proposes an efficient algorithm for removing Gaussian noise from corrupted image by incorporating a wavelet-based trivariate shrinkage filter with a spatial-based joint bilateral filter. In the wavelet domain, the wavelet coefficients are modeled as trivariate Gaussian distribution, taking into account the statistical dependencies among intrascale wavelet coefficients, and then a trivariate shrinkage filter is derived by using the maximum a posteriori (MAP) estimator. Although wavelet-based methods are efficient in image denoising, they are prone to producing salient artifacts such as low-frequency noise and edge ringing which relate to the structure of the underlying wavelet. On the other hand, most spatial-based algorithms output much higher quality denoising image with less artifacts. However, they are usually too computationally demanding. In order to reduce the computational cost, we develop an efficient joint bilateral filter by using the wavelet denoising result rather than directly processing the noisy image in the spatial domain. This filter could suppress the noise while preserve image details with small computational cost. Extension to color image denoising is also presented. We compare our denoising algorithm with other denoising techniques in terms of PSNR and visual quality. The experimental results indicate that our algorithm is competitive with other denoising techniques.     

基于不同预处理方法的多小波暂态信号去噪

在介绍多小波基本理论的基础上,探讨了多小波的不同预处理方法并对多小波滤波器响应产生的影响进行了比较.通过对噪声信号的多小波变换分析,设计基于多小波变换的去噪方法.最后通过大量的仿真工作,对不同预处理方法的多小波与传统小波的电力系统故障暂态信号去噪效果进行了深入分析,结果表明:预处理方法的选择是影响多小波去噪效果的关键因素,若选择合适的预处理方法,利用多小波对暂态信号进行去噪,可以获得比传统小波更好的去噪效果.     

Image denoising with anisotropic bivariate shrinkage

This paper presents a novel image denoising algorithm based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The anisotropic bivariate Laplacian model not only captures the child-parent dependency between wavelet coefficients, but also fits the anisotropic property of the variances of wavelet coefficients in different scales of natural images. With this statistical model, we derive a closed-form anisotropic bivariate shrinkage function in the framework of Bayesian denoising and a new image denoising approach with local marginal variance estimation based on this newly derived shrinkage function is proposed in the discrete wavelet transform (DWT) domain. The proposed anisotropic bivariate shrinkage approach is also extended to the dual-tree complex wavelet transform (DT-CWT) domain to further improve the performance of image denoising. To take full advantage of DT-CWT, a more accurate noise variance estimator is proposed and the way the anisotropic bivariate shrinkage function applied to the magnitudes of DT-CWT coefficients is presented. Experiments were carried out in both the DWT and the DT-CWT domain to validate the effectiveness of the proposed method. Using a representative set of standard test images corrupted by additive white Gaussian noise, the simulation results show that the proposed method provides promising results and is competitive with the best wavelet-based denoising results reported in the literature both in terms of peak signal-to-noise ratio (PSNR) and in visual quality.     

Translation-invariant denoising using multiwavelets

Translation invariant (TI) single wavelet denoising was developed by Coifman and Donoho (1994), and they show that TI is better than non-TI single wavelet denoising. On the other other hand, Strela et al. (1994) have found that non-TI multiwavelet denoising gives better results than non-TI single wavelets. We extend Coifman and Donoho's TI single wavelet denoising scheme to multiwavelets. Experimental results show that TI multiwavelet denoising is better than the single case for soft thresholding     

Building robust wavelet estimators for multicomponent images using Stein's principle.

Multichannel imaging systems provide several observations of the same scene which are often corrupted by noise. In this paper, we are interested in multispectral image denoising in the wavelet domain. We adopt a multivariate statistical approach in order to exploit the correlations existing between the different spectral components. Our main contribution is the application of Stein's principle to build a new estimator for arbitrary multichannel images embedded in additive Gaussian noise. Simulation tests carried out on optical satellite images show that the proposed method outperforms conventional wavelet shrinkage techniques.     

混沌信号的自适应阈值同步挤压小波变换消噪

针对同步挤压小波变换（SST）消噪过程中仅使用单一阈值的不足,对SST消噪时的幅度阈值进行了改进,提出了一种基于SST分层阈值的混沌信号消噪方法.首先,根据信号和噪声经SST分解后系数的分布模型,推导SST混沌去噪时幅度阈值权系数的均方误差计算公式;进而,根据均方误差最小准则,计算幅度阈值权系数的最优取值;最后,根据最优阈值权系数和噪声标准差,确定SST混沌去噪时的分层阈值.利用模拟混沌信号和实测月太阳黑子信号对所提方法进行了实验分析,实验结果表明,本文方法可较好地滤除混沌信号中的噪声,同时原始信号的内在混沌特性也能得到较大程度的恢复.与小波阈值法和集合经验模态分解（EEMD）消噪法相比,可获得更好的消噪效果.     

基于平稳多小波变换的红外图像噪声抑制方法

提出了一种平稳多小波变换方法,该方法结合多小波和平稳小波变换在信号去噪方面的优点,给出了二维图像平稳多小波变换的mallat分解重构算法,并对红外图像的平稳多小波变换系数进行阚值处理实现图像去噪,仿真结果表明,相对于平稳标量小波变换和多小波的噪声抑制方法,此方法对噪声有更好的抑制作用,并尽可能多的保持目标的特征和细节．     

小波变换及其在信号去噪中的应用

介绍了小波变换理论及基于小波变换去除信号噪声的基本原理和方法.研究利用小波变换技术对噪声进行阈值处理和去除非平稳信号的噪声,并应用Matlab软件实现了小波去噪的计算机仿真,仿真结果表明小波变换去除噪声的效果优于传统的Fourier变换.     

基于小波变换的图像去噪方法

针对图像中存在的高斯噪声、椒盐噪声和二者混合噪声,提出了一种基于小波变换的图像去噪方法。为进一步提高图像去噪质量,采用Bayes Shrink和中值滤波相结合的方法,对其的不同去噪顺序进行实验,并与中值滤波、Bayes Shrink方法相比较。实验结果表明,先进行Bayes Shrink再进行中值滤波的方法要优于其他方法,去噪效果较好。在图像去噪处理中该种方法具有实际应用价值。     

基于贝叶斯估计的小波阈值图像降噪方法

提出一种新的基于贝叶斯估计的小波收缩阈值的图像降噪方法,该方法是通过最小Bayes风险的方法对图像小波变换后的小波系数进行估计,这种对小波系数的估计不仅与子带的方向和层次有关,而且与小波系数的大小有关.试验结果表明该方法比一般小波收缩阈值方法的降噪效果要好;还表明在峰值信噪比较低时该方法的降噪效果比Wiener滤波差,当峰值信噪比较高时该方法的降噪效果比Wiener滤波好.     

基于贝叶斯估计的小波阈值图像降噪方法

提出一种新的基于贝叶斯估计的小波收缩阈值的图像降噪方法，该方法是通过最小Bayes风险的方法对图像小波变换后的小波系数进行估计，这种对小波系数的估计不仅与子带的方向和层次有关，而且与小波系数的大小有关。试验结果该方法比一般小波收缩阈值方法的降噪效果要好；还表明在峰值信噪比较低时该方法的降噪效果比Wiener滤波差，当峰值信噪比较高时该方法的降噪效果比Wiener滤波好。     

Shearlet变换域自适应图像去噪算法

首先采用Haar小波滤波器,设计出一种数字Shearlet变换算法。然后对Shearlet系数间的相关性进行统计分析,提出了一种尺度相关的自适应阈值收缩图像去噪算法。最后选用峰值信噪比和视觉质量为评价标准,实验验证算法的去噪性能。结果表明,本文算法获得更高的峰值信噪比,更好地保留了图像的细节信息。     

Color monogenic wavelet transform for multichannel image denoising

This paper proposes an effective color image denoising algorithm using the combination color monogenic wavelet transform (CMWT) with a trivariate shrinkage filter. The CMWT coefficients are one order of magnitude with three phases: two phases encode the local color information while the third contains geometric information relating to texture within the color image. In the CMWT domain, a trivariate Gaussian distribution is applied to capture statistical dependencies between the CMWT coefficients, and then a trivariate shrinkage filter is derived using a maximum a posteriori estimator. The performance of the proposed algorithm is experimentally verified using a variety of color test images with a range of noise levels in terms of PSNR and visual quality. The experimental results demonstrate that the proposed algorithm is equal to or better than current state-of-the-art algorithms in both visual and quantitative performance.     

Optimal FPGA implementation of CL multiwavelets architecture for signal denoising application

Wavelet transform is considered one of the efficient transforms of this decade for real time signal processing. Due to implementation constraints scalar wavelets do not possess the properties such as compact support, regularity, orthogonality and symmetry, which are desirable qualities to provide a good signal to noise ratio (SNR) in case of signal denoising. This leads to the evolution of the new dimension of wavelet called ‘multiwavelets’, which possess more than one scaling and wavelet filters. The architecture implementation of multiwavelets is an emerging area of research. In real time, the signals are in scalar form, which demands the processing architecture to be scalar. But the conventional Donovan Geronimo Hardin Massopust (DGHM) and Chui-Lian (CL) multiwavelets are vectored and are also unbalanced. In this article, the vectored multiwavelet transforms are converted into a scalar form and its architecture is implemented in FPGA (Field Programmable Gate Array) for signal denoising application. The architecture is compared with DGHM multiwavelets architecture in terms of several objective and performance measures. The CL multiwavelets architecture is further optimised for best performance by using DSP48Es. The results show that CL multiwavelet architecture is suited better for the signal denoising application.     

Spatial adaptive Bayesian wavelet threshold exploiting scale and space consistency

Threshold selection is critical in image denoising via wavelet shrinkage. Many powerful approaches have been investigated, but few of them are adaptive to the changing statistics of each subband and meanwhile keep efficiency of the algorithm. In this work, an inter-scale adaptive, data-driven threshold for image denoising via wavelet soft-thresholding is proposed. To get the optimal threshold, a Bayesian estimator is applied to the wavelet coefficients. The threshold is based on the accurate modeling of the distribution of wavelet coefficients using generalized Gaussian distribution (GGD), and the near exponential prior of the wavelet coefficients across scales. The new approach outperforms BayesShrink because it captures the statistical inter-scale property of wavelet coefficients, and is more adaptive to the data of each subband. The simplicity of the proposed threshold makes it easy to achieve the spatial adaptivity, which will further improves the wavelet denoising performance. Simulation results show that higher peak-signal-to-noise ratio can be obtained than other thresholding methods for image denoising.     

基于平衡正交多小波的MR图像去噪算法研究

磁共振图像中的噪声分布的特殊性不仅大大降低了图像的质量,影响医学诊断,而且为噪声的去除提出了更高的要求。平衡正交多小波同时满足正交性和对称性,不仅具有比单小波分解更加精确、去噪效果更好的特点,同时避免了普通多小波分解过程中的预处理过程。文中对磁共振图像进行平衡正交多小波分解后,采用了一种自适应性更高的阈值确定函数与半软阈值相结合方法对小波系数进行萎缩处理,实现降噪目的。结果表明：该方法优于97提升小波及ghm多小波方法,去噪效果进一步提高。     

Genetic algorithm and wavelet hybrid scheme for ECG signal denoising

This paper introduces an effective hybrid scheme for the denoising of electrocardiogram (ECG) signals corrupted by non-stationary noises using genetic algorithm (GA) and wavelet transform (WT). We first applied a wavelet denoising in noise reduction of multi-channel high resolution ECG signals. In particular, the influence of the selection of wavelet function and the choice of decomposition level on efficiency of denoising process was considered. Selection of a suitable wavelet denoising parameters is critical for the success of ECG signal filtration in wavelet domain. Therefore, in our noise elimination method the genetic algorithm has been used to select the optimal wavelet denoising parameters which lead to maximize the filtration performance. The efficiency performance of our scheme is evaluated using percentage root mean square difference (PRD) and signal to noise ratio (SNR). The experimental results show that the introduced hybrid scheme using GA has obtain better performance than the other reported wavelet thresholding algorithms as well as the quality of the denoising ECG signal is more suitable for the clinical diagnosis.     

基于遗传算法的多小波自适应去噪方法研究

针对噪声在多小波分解后的尺度性以及图像本身的特性,提出了一种基于遗传算法的多小波自适应去噪算法,该方法能通过遗传算法自适应地寻求去噪后图像的最小均方误差.实验结果表明,该算法优于传统算法,不仅能有效滤除图像的噪声,而且能较好地保留图像的边缘信息,具有更加理想的去噪效果.