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.     

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.     

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.     

Denoising by singularity detection

A new algorithm for noise reduction using the wavelet transform is proposed. Similar to Mallat's (1992) wavelet transform modulus maxima denoising approach, we estimate the regularity of a signal from the evolution of its wavelet transform coefficients across scales. However, we do not perform maxima detection and processing; therefore, complicated reconstruction is avoided. Instead, the local regularities of a signal are estimated by computing the sum of the modulus of its wavelet coefficients inside the corresponding “cone of influence”, and the coefficients that correspond to the regular part of the signal for reconstruction are selected. The algorithm gives an improved denoising result, as compared with the previous approaches, in terms of mean squared error and visual quality. The new denoising algorithm is also invariant to translation. It does not introduce spurious oscillations and requires very little a priori information of the signal or noise. Besides, we extend the method to two dimensions to estimate the regularity of an image by computing the sum of the modulus of its wavelet coefficients inside the so-called “directional cone of influence”. The denoising technique is applied to tomographic image reconstruction, where the improved performance of the new approach can clearly be observed     

Adaptive wavelet threshold for image denoising

Threshold selection is the critical issue in image denoising via wavelet shrinkage. Many powerful approaches have been investigated, but few have been to make the threshold values adaptive to the changing statistics of images and meanwhile maintain the efficiency of the algorithm. In this work an efficient adaptive algorithm to capture the dependency of inter-scale wavelet coefficients is proposed. Experiments show that higher peak signal-to-noise ratio can be obtained as compared to other threshold-denoising algorithms.     

高分辨率红外图像的分层自适应阈值Curvelet系数萎缩去噪方法

高分辨率红外图像在基于小波系数阈值萎缩的去噪过程中,容易导致边缘模糊或丢失等失真。文中首次引入基于wrapping的第二代快速Curvelet变换,对图像边缘信息进行有效的稀疏保存,并采用分层自适应阈值算法独立估计每个尺度、方向上的Curvelet系数噪声阈值,并针对红外图像的Curvelet系数能量高度集中于低尺度系数的特点,采用尺度相关的硬阈值对染噪图像的Curvelet系数进行处理。实验结果表明：在不同噪声条件下,与基于小波系数的Visu Shrink,Penalized,sparsity-norm阈值等去噪算法相比,文中提出的去噪算法取得了较好的去噪效果,在噪声方差σ=30时,使用该方法的峰值信噪比(PSNR)可高达31.77 dB,去噪后的图像边缘保持良好,具有较好的视觉效果;同时,文中建议算法的计算量比传统Curvelet降低了70%以上,适合在DSP等嵌入式系统应用。     

Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency

Most simple nonlinear thresholding rules for wavelet-based denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependencies. We only consider the dependencies between the coefficients and their parents in detail. For this purpose, new non-Gaussian bivariate distributions are proposed, and corresponding nonlinear threshold functions (shrinkage functions) are derived from the models using Bayesian estimation theory. The new shrinkage functions do not assume the independence of wavelet coefficients. We show three image denoising examples in order to show the performance of these new bivariate shrinkage rules. In the second example, a simple subband-dependent data-driven image denoising system is described and compared with effective data-driven techniques in the literature, namely VisuShrink, SureShrink, BayesShrink, and hidden Markov models. In the third example, the same idea is applied to the dual-tree complex wavelet coefficients.     

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.     

一种自适应小波域图像降噪方法

Donoho所提出的去噪算法由于没有考虑到图像的局部特征,而滤除了过多的小波系数,影响了图像的去噪效果。本文介绍了一种自适应阈值的小波系数收缩算法,该算法利用邻域小波系数与噪声方差关系,同时根据小波分解级数的不同而动态地改变小波系数收缩的幅度。由于阈值的自适应性。从而可以利用更多小波分解级数而不会滤除过多的小波系数,因此在去噪方面达到了更好的效果。本文还讨论了如何选取合适的小波分解级数、窗口大小、以及算法的复杂性。通过大量的实验结果可以看出,本算法在去噪的视觉效果和峰值信噪比(PSNR)指标上,优于其他去噪算法,同时,算法的执行和原理非常简单。     

SURE-LET multichannel image denoising: interscale orthonormal wavelet thresholding.

We propose a vector/matrix extension of our denoising algorithm initially developed for grayscale images, in order to efficiently process multichannel (e.g., color) images. This work follows our recently published SURE-LET approach where the denoising algorithm is parameterized as a linear expansion of thresholds (LET) and optimized using Stein's unbiased risk estimate (SURE). The proposed wavelet thresholding function is pointwise and depends on the coefficients of same location in the other channels, as well as on their parents in the coarser wavelet subband. A nonredundant, orthonormal, wavelet transform is first applied to the noisy data, followed by the (subband-dependent) vector-valued thresholding of individual multichannel wavelet coefficients which are finally brought back to the image domain by inverse wavelet transform. Extensive comparisons with the state-of-the-art multiresolution image denoising algorithms indicate that despite being nonredundant, our algorithm matches the quality of the best redundant approaches, while maintaining a high computational efficiency and a low CPU/memory consumption. An online Java demo illustrates these assertions.     

基于相邻小波系数的图像去噪算法

针对传统的小波去噪方法在滤除噪声上的明显不足,提出了一种基于相邻小波系数的图像去噪算法。充分考虑了滤噪系数与相邻系数间的相关性,首先采用3×3像素的系数滑动窗口对噪声系数进行均值采样,然后结合双阈值法对小波系数进行缩减。实验结果表明本算法明显优于传统的滤波算法,具有较高的信噪比,是一种有效、可行的图像去噪方法。     

多尺度SVR的SAR图像复原

针对合成孔径雷达图像中存在斑点噪声的缺陷,将支持向量拟合方法引入小波系数收缩策略中,提出了基于多尺度SVR(support vector regression)的SAR图像复原算法。该方法在不同尺度下选用不同的核参数。为保护边缘结构信息,首先对各小波高频子带进行SVM拟合,然后计算原始小波系数与拟合估计值的绝对差,并定义小波系数收缩准则,根据准则对小波系数进行收缩,使复原的图像能较好的保持原有图像的纹理和结构信息。实验采用真实的SAR图像,实验结果显示该方法优于常规小波滤波和Lee滤波方法。     

改进小波阈值去噪在PCB图像检测中的应用研究

应用自动光学检测仪检测印刷电路板图像的过程中,图像去噪是至关重要的一个步骤,针对PCB板图像对比度差、动态范围小、图像模糊等问题,提出了一种改进的小波阈值去噪算法。该算法对含噪声的PCB图像进行小波分解,在对分解后不同尺度下的小波系数按照改进的阈值方法进行处理的基础上,进行PCB图像重构。实验结果表明,该方法的均方根误差以及峰值信噪比值均优于传统的软硬阈值去噪方法,是一种有效的图像滤波算法。     

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。     

一种基于幅度预测的隐写分析方法

 提出一种基于图像小波系数相关规律性分析及幅度预测的隐写分析方法,首先对小波系数所处局部区域的相关规律性强弱进行定量分析;然后选择规律性较强的局部区域,利用自然图像小波系数在尺度间和尺度内的统计相关性,以及不同图像分量小波系数之间存在的相关性,对小波系数的幅度值进行自适应预测;最后通过分析预测误差的统计特性来判断图像中是否含有隐秘信息.实验证明该方法对于小波域信息隐藏具有较好的检测效果.     

IMAGE WAVELET DENOISING USING THE ROBUST LOCAL THRESHOLD

This paper suggests a scheme of image denoising based on two-dimensional discrete wavelet transform.The denoising algorithm is described with some operatiors.By thresholding the wavelet transform coefficients of noisy images, the original image can be reconstructed cor-rectly.Different threshold selections and thresholding methods are discussed.A new robust local threshold scheme is proposed.Quantifying the performance of image denoising schemes by using the mean square error, the performance of the robust local threshold scheme is demonstrated and is compared with the universal threshold scheme.The experiment shows that image denoising using the robust local threshold performs better than that using the universal threshold.     

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。     

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.     

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.     

一种图像去噪的小波相位滤波改进算法

大多数的小波去噪方法都是基于图像小波幅度信息的,但对于低SNR图像来说,其小波域中的图像边缘信息被噪声掩盖,所以有人提出了对幅度不敏感的小波相位滤波算法,利用含噪图像分解后的相位信息来恢复图像,本文对这种算法作出了一些改进。在相位滤波的基础上,考虑Laplace邻域,试验结果表明比原算法效果好。