Image denoising via local and nonlocal circulant similarity

A patch based image denoising method is developed in this paper by introducing a new type of image self-similarity. This self-similarity is obtained by cyclic shift, which is called “circulant similarity”. Given a corrupted image patch, it can be estimated by incorporating circulant similarity into a weighted averaging filter. By choosing an appropriate kernel as weight function, the patch filter is implemented by circular convolution, and can be efficiently solved using fast Fourier transform. In addition, the circulant similarity can be enhanced by using nonlocal modeling. We stack the similar image patches into 3D groups, and propose a denoising scheme based on group estimation across the patches. Numerical experiments demonstrate that the proposed method with local circulant similarity outperforms much its local filtering based counterparts, and the proposed method with nonlocal circulant similarity shows very competitive performance with state-of-the-art denoising method, especially on images corrupted by strong noise.     

Image-pair-based deblurring with spatially varying norms and noisy image updating

This paper presents a deblurring method that effectively restores fine textures and details, such as a tree’s leaves or regular patterns, and suppresses noises in flat regions using consecutively captured blurry and noisy images. To accomplish this, we used a method that combines noisy image updating with one iteration and fast deconvolution with spatially varying norms in a modified alternating minimization scheme. The captured noisy image is first denoised with a nonlocal means (NL-means) denoising method, and then fused with a deconvolved version of the captured blurred image on the frequency domain, to provide an initially restored image with less noise. Through a feedback loop, the captured noisy image is directly substituted with the initially restored image for one more NL-means denoising, which results in an upgraded noisy image with clearer outlines and less noise. Next, an alpha map that stores spatially varying norm values, which indicate local gradient priors in a maximum-a-posterior (MAP) estimation, is created based on texture likelihoods found by applying a texture detector to the initially restored image. The alpha map is used in a modified alternating minimization scheme with the pair of upgraded noisy images and a corresponding point spread function (PSF) to improve texture representation and suppress noises and ringing artifacts. Our results show that the proposed method effectively restores details and textures and alleviates noises in flat regions.     

Stochastic image denoising based on Markov-chain Monte Carlo sampling

A novel stochastic approach based on Markov-chain Monte Carlo sampling is investigated for the purpose of image denoising. The additive image denoising problem is formulated as a Bayesian least squares problem, where the goal is to estimate the denoised image given the noisy image as the measurement and an estimated posterior. The posterior is estimated using a nonparametric importance-weighted Markov-chain Monte Carlo sampling approach based on an adaptive Geman-McClure objective function. By learning the posterior in a nonparametric manner, the proposed Markov-chain Monte Carlo denoising (MCMCD) approach adapts in a flexible manner to the underlying image and noise statistics. Furthermore, the computational complexity of MCMCD is relatively low when compared to other published methods with similar denoising performance. The effectiveness of the MCMCD method at image denoising was investigated using additive Gaussian noise, and was found to achieve state-of-the-art denoising performance in terms of both peak signal-to-noise ratio (PSNR) and mean structural similarity (SSIM) metrics when compared to other published methods.     

Speckle noise removal based on structural convolutional neural networks with feature fusion for medical image

Application of convolutional neural networks (CNNs) for image additive white Gaussian noise (AWGN) removal has attracted considerable attentions with the rapid development of deep learning in recent years. However, the work of image multiplicative speckle noise removal is rarely done. Moreover, most of the existing speckle noise removal algorithms are based on traditional methods with human priori knowledge, which means that the parameters of the algorithms need to be set manually. Nowadays, deep learning methods show clear advantages on image feature extraction. Multiplicative speckle noise is very common in real life images, especially in medical images. In this paper, a novel neural network structure is proposed to recover noisy images with speckle noise. Our proposed method mainly consists of three subnetworks. One network is rough clean image estimate subnetwork. Another is subnetwork of noise estimation. The last one is an information fusion network based on U-Net and several convolutional layers. Different from the existing speckle denoising model based on the statistics of images, the proposed network model can handle speckle denoising of different noise levels with an end-to-end trainable model. Extensive experimental results on several test datasets clearly demonstrate the superior performance of our proposed network over state-of-the-arts in terms of quantitative metrics and visual quality.     

An MMSE approach to nonlocal image denoising: Theory and practical implementation

A nonlocal minimum mean square error (MMSE) image denoising algorithm is proposed in this work. Based on the Bayesian estimation theory, we first derive that the conventional nonlocal means filter is an MMSE estimator in the special case of noise-free nonlocal neighbors. Then, we develop the nonlocal MMSE denoising filter that can minimize the mean square error (MSE) of a denoised block in more general cases of noisy nonlocal neighbors. Furthermore, the proposed algorithm searches nonlocal neighbors from an external database as well as the entire input image to improve the performance even when a noisy block may not have similar blocks within the image. Since the extended search range demands a higher computational burden, we develop a probabilistic tree-based search method to reduce the computational complexity. Simulation results show that the proposed algorithm provides significantly better denoising performance than the conventional nonlocal means filter.     

Combining self-learning based super-resolution with denoising for noisy images

In this paper, we propose a new learning based joint Super-Resolution (SR) and denoising algorithm for noisy images. The individual processing of denoising and SR when super-resolving a noisy image has drawbacks such as noise amplification, blurring and SR performance reduction. In the proposed joint method, principal component analysis (PCA) based denoising is closely combined with a self-learning SR framework in order to minimize the SR visual quality degradation caused by noise. Experimental results show that the joint method achieves an SR image quality improvement in terms of noise and blurring, when compared with the state-of-the-art joint method and sequential combinations of individual denoising and SR.     

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。     

Gray-level image denoising with an improved weighted sparse coding

The nonlocal self-similarity of images means that groups of similar patches have low-dimensional property. The property has been previously used for image denoising, with particularly notable success via sparse coding. However, only a few studies have focused on the varying statistics of noise in different similar patches during the iterative denoising process. This has motivated us to introduce an improved weighted sparse coding for gray-level image denoising in this paper. On the basis of traditional sparse coding, we introduce a weight matrix to account for the noise variation characteristics of different similar patches, while introduce another weight matrix to make full use of the sparsity priors of natural images. The Maximum A-Posterior estimation (MAP) is used to obtain the closed-form solution of the proposed method. Experimental results demonstrate the competitiveness of the proposed method compared with that of state-of-the-art methods in both the objective and perceptual quality.     

Gabor feature based nonlocal means filter for textured image denoising

The nonlocal means (NLM) filter has distinct advantages over traditional image denoising techniques. However, in spite of its simplicity, the pixel value-based self-similarity measure used by the NLM filter is intrinsically less robust when applied to images with non-stationary contents. In this paper, we use Gabor-based texture features to measure the self-similarity, and thus propose the Gabor feature based NLM (GFNLM) filter for textured image denoising. This filter recovers noise-corrupted images by replacing each pixel value with the weighted sum of pixel values in its search window, where each weight is defined based on the Gabor-based texture similarity measure. The GFNLM filter has been compared to the classical NLM filter and four other state-of-the-art image denoising algorithms in textured images degraded by additive Gaussian noise. Our results show that the proposed GFNLM filter can denoise textured images more effectively and robustly while preserving the texture information.     

Multi-stage image denoising based on correlation coefficient matching and sparse dictionary pruning

We present a novel image denoising method based on multiscale sparse representations. In tackling the conflicting problems of structure extraction and artifact suppression, we introduce a correlation coefficient matching criterion for sparse coding so as to extract more meaningful structures from the noisy image. On the other hand, we propose a dictionary pruning method to suppress noise. Based on the above techniques, an effective dictionary training method is developed. To further improve the denoising performance, we propose a multi-stage sparse coding framework where sparse representations are obtained in different scales to capture multiscale image features for effective denoising. The multi-stage coding scheme not only reduces the computational burden of previous multiscale denoising approaches, but more importantly, it also contributes to artifact suppression. Experimental results show that the proposed method achieves a state-of-the-art denoising performance in terms of both objective and subjective quality and provides significant improvements over other methods at high noise levels.     

An image denoising algorithm for mixed noise combining nonlocal means filter and sparse representation technique

Nonlocal means (NLM) filtering or sparse representation based denoising method has obtained a remarkable denoising performance. In order to integrate the advantages of two methods into a unified framework, we propose an image denoising algorithm through skillfully combining NLM and sparse representation technique to remove Gaussian noise mixed with random-valued impulse noise. In the non-Gaussian circumstance, we propose a customized blockwise NLM (CBNLM) filter to generate an initial denoised image. Based on it, we classify the different noisy pixels according to the three-sigma rule. Besides, an overcomplete dictionary is trained on the initial denoised image. Then, a complementary sparse coding technique is used to find the sparse vector for each input noisy patch over the overcomplete dictionary. Through solving a more reasonable variational denoising model, we can reconstruct the clean image. Experimental results verify that our proposed algorithm can obtain the best denoising performance, compared with some typical methods.     

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.     

基于曲波域的指纹预处理研究

研究了一种基于曲波域的指纹图像预处理方法。首先将指纹图像在曲波域中分解,然后用Gabor滤波器来处理粗尺度系数,这些系数是原图像的近似值;同时,在细尺度系数上使用软阈值函数减少沿着脊线方向的噪声。再将重构以后的图像二值化,最后使用基于模板的脉冲耦合神经网络(PCNNs)细化算法细化二值图像,得到指纹的骨架图像。实验结果表明,该方法优于传统的基于Gabor滤波器的指纹图像预处理方法。     

带曲波域约束的全变差正则化抑噪方法

为了减小曲波变换在图像抑噪应用中所出现的伪吉布斯振荡和"曲波状"伪曲线,提出一种融合计算调和分析与变分法的图像抑噪方法.首先引入第二代曲波紧框架,对降质图像进行非线性曲波变换阈值,然后由所保留系数确定可行域,建立带曲波域约束条件的全变差正则化模型,最后通过投影梯度算法进行求解.实验结果表明该方法在抑噪和保持边缘的同时,使这些失真得到有效地抑制,取得了较为理想的视觉效果.     

Denoising by low-rank and sparse representations

Due to the ill-posed nature of image denoising problem, good image priors are of great importance for an effective restoration. Nonlocal self-similarity and sparsity are two popular and widely used image priors which have led to several state-of-the-art methods in natural image denoising. In this paper, we take advantage of these priors and propose a new denoising algorithm based on sparse and low-rank representation of image patches under a nonlocal framework. This framework consists of two complementary steps. In the first step, noise removal from groups of matched image patches is formulated as recovery of low-rank matrices from noisy data. This problem is then efficiently solved under asymptotic matrix reconstruction model based on recent results from random matrix theory which leads to a parameter-free optimal estimator. Nonlocal learned sparse representation is adopted in the second step to suppress artifacts introduced in the previous estimate. Experimental results, demonstrate the superior denoising performance of the proposed algorithm as compared with the state-of-the-art methods.     

A nonsubsampled countourlet transform based CNN for real image denoising

The state of the art deep learning based denoising methods can achieve great denoising results. However, due to the lack of clean training data, the ground truth and noise level are unknown, traditional denoising methods are difficult to remove blind noise in general images. Furthermore, deep learning methods require specific noise levels to train the model, and specific models are built only deal with one noise level. In this paper, we propose a Nonsubsampled Countourlet Transform based convolutional network model (CTCNN) to deal with Gaussian noise and the noise of real images. The model is modified by U-Net, nonsubsampled Countourlet Transform (NSCT) and inverse NSCT are used to instead of sum pooling layer and up-convolution operation. NSCT can decrease the size of feature maps and preserve details of images without information loss. Different training strategies are adopted to train models in order to handle blinding noise such as underwater images which contain noise naturally. Simulation results show the proposed method is effective in standard images dataset and blind noisy images. The model we proposed has been compared with other state of the art denoising methods, and better subjective representation and PSNR improvement are obtained.     

Image denoising by supervised adaptive fusion of decomposed images restored using wave atom,curvelet and wavelet transform

This paper presents an efficient image denoising method that adaptively combines the features of wavelets, wave atoms and curvelets. Wavelet shrinkage is used to denoise the smooth regions in the image while wave atoms are employed to denoise the textures, and the edges will take advantage of curvelet denoising. The received noisy image is firstly decomposed into a homogenous (smooth/cartoon) part and a textural part. The cartoon part of the noisy image is denoised using wavelet transform, and the texture part of the noisy image is denoised using wave atoms. The two denoised images are then fused adaptively. For adaptive fusion, different weights are chosen from the variance map of the denoised texture image. Further improvement in denoising results is achieved by denoising the edges through curvelet transform. The information about edge location is gathered from the variance map of denoised cartoon image. The denoised image results in perfect presentation of the smooth regions and efficient preservation of textures and edges in the image.     

基于稀疏分解的指静脉图像去噪

手指静脉识别技术因其独特的优势,受到广泛的关注。然而由硬件系统获取的手指静脉图像常常含有严重的噪声、阴影等问题,所以对低质量的静脉图像的去噪成为了整个识别过程的关键。本文提出了一种基于稀疏分解的指静脉图像去噪新方法。基于稀疏分解的图像去噪是将含有噪声的图像信息进行稀疏分解,分解成稀疏成分和其他成分。其中的稀疏部分是有用信息,其他部分被认为是噪声,再由图像的稀疏部分重建原始信号,达到恢复原始信号并去除噪声的效果。本文根据指静脉图像的静脉的特点,应用高斯函数构造了过完备库。用合成图像和真实指静脉图像分别对新算法进行实验验证。实验结果证明,与传统的去噪算法相比,峰值信噪比提高1-2dB。      

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。     

基于模糊划分的曲波和小波降噪算法研究

针对曲波降噪方法在获得高质量图像的同时会出现一些虚像的问题,提出了一种用来抑制虚像的基于模糊划分的降噪算法?算法基于结果图像的曲波和隐藏马 尔科夫树的降噪方式设计,图像经过模糊划分后,模糊窗口的性能可以估算,而基于曲波和小波结果图像的图像融合权值可以由模糊窗口的性能确定?试验结果证明,文中算法能有效地提高结果图像的视觉效果并能明显地抑制结果图 像的虚像?