Image denoising based on non-local means filter and its method noise thresholding

Non-local means filter uses all the possible self-predictions and self-similarities the image can provide to determine the pixel weights for filtering the noisy image, with the assumption that the image contains an extensive amount of self-similarity. As the pixels are highly correlated and the noise is typically independently and identically distributed, averaging of these pixels results in noise suppression thereby yielding a pixel that is similar to its original value. The non-local means filter removes the noise and cleans the edges without losing too many fine structure and details. But as the noise increases, the performance of non-local means filter deteriorates and the denoised image suffers from blurring and loss of image details. This is because the similar local patches used to find the pixel weights contains noisy pixels. In this paper, the blend of non-local means filter and its method noise thresholding using wavelets is proposed for better image denoising. The performance of the proposed method is compared with wavelet thresholding, bilateral filter, non-local means filter and multi-resolution bilateral filter. It is found that performance of proposed method is superior to wavelet thresholding, bilateral filter and non-local means filter and superior/akin to multi-resolution bilateral filter in terms of method noise, visual quality, PSNR and Image Quality Index.     

Image denoising based on gaussian/bilateral filter and its method noise thresholding

The Gaussian filter is a local and linear filter that smoothes the whole image irrespective of its edges or details, whereas the bilateral filter is also a local but non-linear, considers both gray level similarities and geometric closeness of the neighboring pixels without smoothing edges. The extension of bilateral filter: multi-resolution bilateral filter, where bilateral filter is applied to approximation subbands of an image decomposed and after each level of wavelet reconstruction. The application of bilateral filter on the approximation subband results in loss of some image details, whereas that after each level of wavelet reconstruction flattens the gray levels thereby resulting in a cartoon-like appearance. To tackle these issues, it is proposed to use the blend of Gaussian/bilateral filter and its method noise thresholding using wavelets. In Gaussian noise scenarios, the performance of proposed methods is compared with existing denoising methods and found that, it has inferior performance compared to Bayesian least squares estimate using Gaussian Scale mixture and superior/comparable performance to that of wavelet thresholding, bilateral filter, multi-resolution bilateral filter, NL-means and Kernel based methods. Further, proposed methods have the advantage of less computational time compared to other methods except wavelet thresholding, bilateral filter.     

一种小波域与空域相结合的图像滤波方法

利用小波阈值去噪方法和传统空间域Lee 滤波的特点, 提出了一种图像去噪的的组合滤波方案。首先在小波域对图像阈值去噪, 得到预去噪图像; 再在空间域上利用自适应Wiener 滤波器进一步提高恢复图像的精度。为了保证小波域和空间域两种算法之间的匹配, 对预去噪图像中残留噪声的分布进行了研究, 对其噪声方差估计做了改进, 提出了一种估计噪声方差的近似最优公式。仿真实验表明, 与单独的在小波域或空域去噪相比, 该方法的均方误差和信噪比指标均得到了改善。     

一种小波域与空域相结合的图像滤波方法

利用小波阈值去噪方法和传统空间域Lee滤波的特点,提出了一种图像去噪的的组合滤波方案。首先在小波域对图像阈值去噪,得到预去噪图像;再在空间域上利用自适应Wiener滤波器进一步提高恢复图像的精度。为了保证小波域和空间域两种算法之间的匹配,对预去噪图像中残留噪声的分布进行了研究,对其噪声方差估计做了改进,提出了一种估计噪声方差的近似最优公式。仿真实验表明,与单独的在小波域或空域去噪相比,该方法的均方误差和信噪比指标均得到了改善。     

Wavelet thresholding of multivalued images

In this paper, a denoising technique for multivalued images exploiting interband correlations is proposed. A redundant wavelet transform is applied and denoising is applied by thresholding wavelet coefficients. Specific functions of the wavelet coefficients are defined that exploit interscale and/or interband correlation of the signal. Three functions are studied: the square of the wavelet coefficients, products of coefficients at adjacent scales, and products of coefficients from different bands. For these functions, the signal and noise probability density functions (pdf) become more separated. The high signal correlation between bands is exploited by summing these products over all bands, in this way separating noise and signal pdfs even more. The noise pdf of the proposed quantities is derived analytically and from this, a wavelet threshold is derived. The technique is demonstrated to outperform single band wavelet thresholding on multispectral remote sensing images and on multimodal MRI images.     

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.     

基于小波影响锥分析的图像去噪方法

采用非抽取小波变换(UDWT),在小波影响锥(COI)分析的基础上,提出一种新的图像去噪方法,能够有效地去除脉冲噪声同时保护图像的边缘.该方法与传统小波阈值去噪法结合,可以很好地抑制高斯噪声和泊松噪声,甚至混合形式的噪声.实验结果证实了该方法的有效性.     

Multiresolution Bilateral Filtering for Image Denoising

The bilateral filter is a nonlinear filter that does spatial averaging without smoothing edges; it has shown to be an effective image denoising technique. An important issue with the application of the bilateral filter is the selection of the filter parameters, which affect the results significantly. There are two main contributions of this paper. The first contribution is an empirical study of the optimal bilateral filter parameter selection in image denoising applications. The second contribution is an extension of the bilateral filter: multiresolution bilateral filter, where bilateral filtering is applied to the approximation (low-frequency) subbands of a signal decomposed using a wavelet filter bank. The multiresolution bilateral filter is combined with wavelet thresholding to form a new image denoising framework, which turns out to be very effective in eliminating noise in real noisy images. Experimental results with both simulated and real data are provided.      

基于噪声分离和小波阈值自适应图像去噪算法

针对VisuShrink小波阈值滤波算法的不足和混合噪声的情况,提出了一种基于噪声分离和尺度的自适应混合图像去噪算法.算法首先通过极值检测分离脉冲噪声和高斯噪声,然后分别对脉冲噪声应用多窗口中值滤波及高斯噪声应用基于尺度的小波阈值滤波完成去噪.实验表明,该混合滤波算法能有效去除图像中的脉冲噪声和高斯噪声,并较好地保存了...     

用小波变换抑制SAR图像中的斑点噪声

抑制合成孔径雷达图像中的斑点噪声一直是处理图像并得到准确图像信息的难点，提出了一种基于小波变换抑制合成孔径雷达（SAR）图像中的斑点噪声的方法，对原有的小波变换方法作了改进，能更好地保留图像的边缘信息，并能简化计算量。在仿真实验中使用了合成的模拟图像和真实的合成孔径雷图像，并与以往的小波去噪滤波方法以及一些经典的斑点噪声滤波方法（包括中值滤波，Lee滤波，Frost滤波）进行比较，在综合考虑了滤波算法在均匀区域对斑点噪声的抑制能力以及保留边缘信息能力的情况下，提出的算法有更好的效果。     

一种自适应多尺度积阈值的图像去噪算法

该文提出了平稳小波变换(Stationary Wavelet Transform, SWT )域自适应多尺度积阈值的图像去噪算法(SWT domain Multiscale Products, SWTMP)。与传统的阈值去噪算法不同,该阈值不是直接作用于小波系数,而是作用于小波系数的空间多尺度积。分析了SWT域含噪图像多尺度积的特点,提出了SWT域自适应多尺度积阈值的计算方法。多尺度积强化了图像的重要结构信息,弱化了噪声,在有效去噪的同时更多地保留了图像的边缘和细节。实验结果表明,所提算法对自然图像去噪后的视觉效果和性能指标均好于二进小波域多尺度积阈值(Adaptive Multiscale Products Thresholding, AMPT)去噪方法。     

Development of EMD-Based Denoising Methods Inspired by Wavelet Thresholding

One of the tasks for which empirical mode decomposition (EMD) is potentially useful is nonparametric signal denoising, an area for which wavelet thresholding has been the dominant technique for many years. In this paper, the wavelet thresholding principle is used in the decomposition modes resulting from applying EMD to a signal. We show that although a direct application of this principle is not feasible in the EMD case, it can be appropriately adapted by exploiting the special characteristics of the EMD decomposition modes. In the same manner, inspired by the translation invariant wavelet thresholding, a similar technique adapted to EMD is developed, leading to enhanced denoising performance.      

基于小波变换的红外图像去噪

提出一种基于新型阈值函数的小波域红外图像去噪法,其阈值函数表达式简单且连续,既克服了硬阈值函数不连续的缺点,又克服了软阈值函数中估计小波系数与含噪小波系数间存在恒定偏差的缺陷。同时新的阈值函数还有效地利用了小波系数的成串性,即在小波系数的估计计算中考虑了邻域小波系数的大小。仿真结果表明,在去噪红外图像视觉效果和峰值信噪比两个方面,文中提出的去噪法优于已有的各种门限去噪法和Matlab-wiener2滤波算法。     

Wavelet-based image estimation: an empirical Bayes approach usingJeffrey''s noninformative prior

The sparseness and decorrelation properties of the discrete wavelet transform have been exploited to develop powerful denoising methods. However, most of these methods have free parameters which have to be adjusted or estimated. In this paper, we propose a wavelet-based denoising technique without any free parameters; it is, in this sense, a "universal" method. Our approach uses empirical Bayes estimation based on a Jeffreys' noninformative prior; it is a step toward objective Bayesian wavelet-based denoising. The result is a remarkably simple fixed nonlinear shrinkage/thresholding rule which performs better than other more computationally demanding methods.     

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.     

Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising.

We develop three novel wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. The core of our approach is the estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest." In this respect, we analyze cases where the probability of signal presence is 1) fixed per subband, 2) conditioned on a local spatial context, and 3) conditioned on information from multiple image bands. All the probabilities are estimated assuming a generalized Laplacian prior for noise-free subband data and additive white Gaussian noise. The results demonstrate that the new subband-adaptive shrinkage function outperforms Bayesian thresholding approaches in terms of mean-squared error. The spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity. The performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding.     

基于小波阈值去噪和共轭模糊函数的时频差联合估计算法

为了解决二阶互模糊函数对相关噪声处理的局限性问题,以及基于四阶累积量的联合估计算法的运算量大的问题,该文利用小波阈值去噪方法结合非圆信号的特性,提出一种新的时频差联合估计算法。该方法首先对接收信号进行小波阈值去噪,然后构造共轭模糊函数,最后再进行2维搜索,得到时差和频差参数。仿真实验给出不同信噪比下的参数估计结果,得出这种算法能抑制相关噪声,又能相对降低运算复杂度,并且在较低信噪比下也能做出准确估计。     

Efficient image denoising method based on a new adaptive wavelet packet thresholding function

This paper proposes a statistically optimum adaptive wavelet packet (WP) thresholding function for image denoising based on the generalized Gaussian distribution. It applies computationally efficient multilevel WP decomposition to noisy images to obtain the best tree or optimal wavelet basis, utilizing Shannon entropy. It selects an adaptive threshold value which is level and subband dependent based on analyzing the statistical parameters of subband coefficients. In the utilized thresholding function, which is based on a maximum a posteriori estimate, the modified version of dominant coefficients was estimated by optimal linear interpolation between each coefficient and the mean value of the corresponding subband. Experimental results, on several test images under different noise intensity conditions, show that the proposed algorithm, called OLI-Shrink, yields better peak signal noise ratio and superior visual image quality-measured by universal image quality index-compared to standard denoising methods, especially in the presence of high noise intensity. It also outperforms some of the best state-of-the-art wavelet-based denoising techniques.     

双Haar小波变换系数的MAP估计及在图像去噪中的应用

小波变换作为一种新的工具,在信号去噪中得到了重要的应用。本文对双Haar小波变换系数,提出了MAP的估计方法,并对其在图像去噪中的应用进行了讨论。实验表明所提出的小波收缩算法与软门限方法相比较,用于图像去噪时可以给出更好的结果。     

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.