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.     

Feature-based wavelet shrinkage algorithm for image denoising.

A selective wavelet shrinkage algorithm for digital image denoising is presented. The performance of this method is an improvement upon other methods proposed in the literature and is algorithmically simple for large computational savings. The improved performance and computational speed of the proposed wavelet shrinkage algorithm is presented and experimentally compared with established methods. The denoising method incorporated in the proposed algorithm involves a two-threshold validation process for real-time selection of wavelet coefficients. The two-threshold criteria selects wavelet coefficients based on their absolute value, spatial regularity, and regularity across multiresolution scales. The proposed algorithm takes image features into consideration in the selection process. Statistically, most images have regular features resulting in connected subband coefficients. Therefore, the resulting subbands of wavelet transformed images in large part do not contain isolated coefficients. In the proposed algorithm, coefficients are selected due to their magnitude, and only a subset of those selected coefficients which exhibit a spatially regular behavior remain for image reconstruction. Therefore, two thresholds are used in the coefficient selection process. The first threshold is used to distinguish coefficients of large magnitude and the second is used to distinguish coefficients of spatial regularity. The performance of the proposed wavelet denoising technique is an improvement upon several other established wavelet denoising techniques, as well as being computationally efficient to facilitate real-time image-processing applications.     

Multiresolution Image Representation Using Combined 2-D and 1-D Directional Filter Banks

In this paper, effective multiresolution image representations using a combination of 2-D filter bank (FB) and directional wavelet transform (WT) are presented. The proposed methods yield simple implementation and low computation costs compared to previous 1-D and 2-D FB combinations or adaptive directional WT methods. Furthermore, they are nonredundant transforms and realize quad-tree like multiresolution representations. In applications on nonlinear approximation, image coding, and denoising, the proposed filter banks show visual quality improvements and have higher PSNR than the conventional separable WT or the contourlet.     

Smoothing low-SNR molecular images via anisotropic median-diffusion

We propose a new anisotropic diffusion filter for denoising low-signal-to-noise molecular images. This filter, which incorporates a median filter into the diffusion steps, is called an anisotropic median-diffusion filter. This hybrid filter achieved much better noise suppression with minimum edge blurring compared with the original anisotropic diffusion filter when it was tested on an image created based on a molecular image model. The universal quality index, proposed in this paper to measure the effectiveness of denoising, suggests that the anisotropic median-diffusion filter can retain adherence to the original image intensities and contrasts better than other filters. In addition, the performance of the filter is less sensitive to the selection of the image gradient threshold during diffusion, thus making automatic image denoising easier than with the original anisotropic diffusion filter. The anisotropic median-diffusion filter also achieved good denoising results on a piecewise-smooth natural image and real Raman molecular images.     

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.     

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 wavelets and multifractals for singularity detection.

This paper presents a very efficient algorithm for image denoising based on wavelets and multifractals for singularity detection. A challenge of image denoising is how to preserve the edges of an image when reducing noise. By modeling the intensity surface of a noisy image as statistically self-similar multifractal processes and taking advantage of the multiresolution analysis with wavelet transform to exploit the local statistical self-similarity at different scales, the pointwise singularity strength value characterizing the local singularity at each scale was calculated. By thresholding the singularity strength, wavelet coefficients at each scale were classified into two categories: the edge-related and regular wavelet coefficients and the irregular coefficients. The irregular coefficients were denoised using an approximate minimum mean-squared error (MMSE) estimation method, while the edge-related and regular wavelet coefficients were smoothed using the fuzzy weighted mean (FWM) filter aiming at preserving the edges and details when reducing noise. Furthermore, to make the FWM-based filtering more efficient for noise reduction at the lowest decomposition level, the MMSE-based filtering was performed as the first pass of denoising followed by performing the FWM-based filtering. Experimental results demonstrated that this algorithm could achieve both good visual quality and high PSNR for the denoised images.     

Bilateral filtering with adaptation to phase coherence and noise

In this paper, a bilateral filter with adaptive domain and range parameter is introduced for image denoising. Since the objective of denoising is to reduce noise as much as possible while preserving the perceptually important details, the parameters are adjusted in accordance with perceptual significance of pixels and noise level. The domain parameter is obtained by using the maximum and minimum moments of local phase coherence for being the representative of image details such as edges and corners of an image. The range parameter is estimated from the intensity-homogeneity measurements for their ability to represent the underlying noise. In addition, the filter is applied in an iterative manner to reduce the residual noise. Experiments are carried out using various standard images, and the results show that the proposed method is more effective in reducing additive white Gaussian noise as compared to several recently introduced denoising techniques in terms of the peak signal-to-noise ratio, structural similarity index and visual quality. In addition, experiments performed using real noisy images reveal the ability of the proposed filter to provide denoised images of better visual quality.     

基于提升小波变换和中值滤波的图像去噪方法研究

针对实际拍摄的背景复杂、目标对比度和信噪比低的图像,在综合考滤图像去噪平滑效果、图像清晰程度和时间复杂度的基础上,提出一种基于提升小波变换和中值滤波的图像去噪方法.首先对含噪图像进行提升小波分解,再在图像高频部分进行中值滤波以改善图像的消噪效果,最后采用信噪比(SNR)与均方根误差(RMSE)和图像灰度曲面图作为图像去噪效果的评估,将提升小波变换和中值滤波相结合的图像去噪方法与小波去噪、小波与中值滤波结合消噪等进行对比实验.实验结果表明,该方法既能消除图像噪声又能达到保持其图像边缘要求,且时间度较低.     

基于经验模分解的小波阈值滤波方法研究

信号的多分辨经验模分解方法可以解释为以信号极值特征尺度为度量的时空滤波过程。这种时空滤波器充 分保留了信号本身的非线性和非平稳特征,在信号的滤波和去噪中具有较大的优势。本文提出了一种基于经验模分解的小 波阈值滤波去噪方法,并和小波阈值去噪、多尺度EMD滤波效果相比较。实验结果表明了基于经验模分解的小波阈值去 噪具有广泛的适用性和独特的去除非平稳信号的有色噪声的优势。     

一种适用于图象去噪的三通道正交完全重建滤波器组

小波变换作为一种多尺度信号分析方法,在图像处理中得到了重要的应用.图像处理的一个重要研究方向就是去噪.由于图像含有大量的边缘,因此用于图像处理的小波基必须具有良好的边缘检测性能和较强的平滑噪声能力.但是,目前还难以找到具有这样特性的正交小波基.本文利用信号的多相位表示理论,提出了一种基于Haar小波的三通道正交完全重建滤波器组,并推导出它在图像去噪中的软门限方法.试验表明,该滤波器组用于图像去噪可以得到很好的结果.     

Optimal spatial adaptation for patch-based image denoising.

A novel adaptive and patch-based approach is proposed for image denoising and representation. The method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel. Our contribution is to associate with each pixel the weighted sum of data points within an adaptive neighborhood, in a manner that it balances the accuracy of approximation and the stochastic error, at each spatial position. This method is general and can be applied under the assumption that there exists repetitive patterns in a local neighborhood of a point. By introducing spatial adaptivity, we extend the work earlier described by Buades et al. which can be considered as an extension of bilateral filtering to image patches. Finally, we propose a nearly parameter-free algorithm for image denoising. The method is applied to both artificially corrupted (white Gaussian noise) and real images and the performance is very close to, and in some cases even surpasses, that of the already published denoising methods.     

Multiresolution reconstruction in fan-beam tomography

In this paper, a new multiresolution reconstruction approach for fan-beam tomography is established. The theoretical development assumes radial wavelets. An approximate reconstruction formula based on a near-radial quincunx multiresolution scheme is proposed. This multiresolution algorithm allows to compute both the quincunx approximation and detail coefficients of an image from its fan-beam projections. Simulations on mathematical phantoms show that wavelet decomposition is acceptable for small beam angles but deteriorates at high angles. The main applications of the method are denoising and wavelet-based image analysis.     

Moving window-based double Haar wavelet transform for image processing.

Image denoising is a lively research field. The classical nonlinear filters used for image denoising, such as median filter, are based on a local analysis of the pixels within a moving window. Recently, the research of image denoising has been focused on the wavelet domain. Compared to the classical nonlinear filters, it is based on a global multiscale analysis of images. Apparently, the wavelet transform can be embedded in a moving window. Thus, a moving window-based local multiscale analysis is obtained. In this paper, based on the Haar wavelet, a class of nonorthogonal multi-channel filter bank with its corresponding wavelet shrinkage called Lee shrinkage is derived. As a special case of this filter bank, the double Haar wavelet transform is introduced. Examples show that it is suitable for a moving window-based local multiscale analysis used for image denoising, edge detection, and edge enhancement.     

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。     

Adaptive image denoising using scale and space consistency

This paper proposes a new method for image denoising with edge preservation, based on image multiresolution decomposition by a redundant wavelet transform. In our approach, edges are implicitly located and preserved in the wavelet domain, whilst image noise is filtered out. At each resolution level, the image edges are estimated by gradient magnitudes (obtained from the wavelet coefficients), which are modeled probabilistically, and a shrinkage function is assembled based on the model obtained. Joint use of space and scale consistency is applied for better preservation of edges. The shrinkage functions are combined to preserve edges that appear simultaneously at several resolutions, and geometric constraints are applied to preserve edges that are not isolated. The proposed technique produces a filtered version of the original image, where homogeneous regions appear separated by well-defined edges. Possible applications include image presegmentation, and image denoising.     

Optimum filter banks for signal decomposition and its applicationin adaptive echo cancellation

The application of multirate filter banks in echo cancellation is investigated. The multiresolution algorithm is used to decompose the received sampling sequence into a number of components, and then, an adaptive algorithm is applied to cancel the echo in the received signal. In this paper, the performance of this method is discussed, from which optimal conditions for echo cancellation are established for the design of wavelet packet multiresolution decomposition. An efficient algorithm for designing such a set of optimal discrete filter banks is developed. The cases of optimal in-band and adjacent-band adaptive filtering are examined. Experimental results showed that the use of optimally designed multiresolution filter banks coupled with in-band or adjacent-band adaptive filtering is much more effective than the employment of commonly used wavelet filter banks. Furthermore, the use of the adjacent-band adaptive filtering algorithm has superior performance compared with that of the in-band filtering     

基于FPGA的红外图像细节增强算法设计与实现

双边滤波算法是一种有效的红外图像细节增强算法,具有保边去噪的效果。但由于算法运算量大,在红外视频图像处理中较难实现。本文提出了一种双边滤波+平台直方图均衡的红外图像增强算法的FPGA实现方法,选用Xilinx Virtex-5系列芯片,采用流水线和并行处理技术,能够在40 ms内完成一帧640×480的14位图像的处理,有效提升红外图像的清晰度和对比度,并满足视频图像处理算法的实时性要求。     

基于多级中值滤波—提升小波技术的图像去噪

针对实际图像含有椒盐噪声及高斯噪声等混合噪声,在中值滤波基础上,采用一种改进型多级中值滤波技术抑制椒盐噪声。首先构造多级中值滤波器,找出混合噪声的位置分布矩阵,然后对含噪图像进行多级中值滤波;同时,对原始小波进行提升,构造提升小波,采用提升小波自适应阈值去噪方法抑制高斯噪声。对含不同混合噪声图像进行去噪实验。结果表明：采用本文方法,计算速度快,提高了图像信噪比,图像细节边缘保护能力强,混合噪声得到有效抑制,去噪效果好。     

基于四元数小波变换域统计模型的图像去噪

图像去噪是图像处理的基本问题,四元数小波变换是1种新的多尺度分析工具.图像经四元数小波变换后,其小波系数不仅在尺度间具有相关性,而且在尺度内也具有一定的相关性.首先利用层内及层间的相关性,用非高斯分布对四元数小波系数进行建模,然后给出分类准则,把小波系数分类为重要系数和不重要系数,再用非高斯分布模型对重要系数与其邻域系...