Joint demosaicing and denoising.

The output image of a digital camera is subject to a severe degradation due to noise in the image sensor. This paper proposes a novel technique to combine demosaicing and denoising procedures systematically into a single operation by exploiting their obvious similarities. We first design a filter as if we are optimally estimating a pixel value from a noisy single-color (sensor) image. With additional constraints, we show that the same filter coefficients are appropriate for color filter array interpolation (demosaicing) given noisy sensor data. The proposed technique can combine many existing denoising algorithms with the demosaicing operation. In this paper, a total least squares denoising method is used to demonstrate the concept. The algorithm is tested on color images with pseudorandom noise and on raw sensor data from a real CMOS digital camera that we calibrated. The experimental results confirm that the proposed method suppresses noise (CMOS/CCD image sensor noise model) while effectively interpolating the missing pixel components, demonstrating a significant improvement in image quality when compared to treating demosaicing and denoising problems independently.     

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.     

Curvelet based nonlocal means algorithm for image denoising

In this work, a curvelet based nonlocal means denoising method is proposed. In the proposed method, the curvelet transform is firstly implemented on the noisy image to produce reconstructed images. Then the similarity of two pixels in the noisy image is computed based on these reconstructed images which include complementary image features at relatively high noise levels or both the reconstructed images and the noisy image at relatively low noise levels. Finally, the pixel similarity and the noisy image are utilized to obtain the final denoised result using the nonlocal means method. Quantitative and visual comparisons demonstrate that the proposed method outperforms the state-of-art nonlocal means denoising methods in terms of noise removal and detail preservation.     

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.     

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.     

Image denoising and quality measurements by using filtering and wavelet based techniques

An image is often corrupted by noise in its acquisition and transmission by various kinds of noises. Image denoising using thresholding methods find appropriate values (threshold) which separates noise values to actual image values without affecting the significant features of the image. Wavelet transform represents image energy in compact form and representation helps in determining threshold between noisy features and important image feature. In this paper we have worked with denoising of salt–pepper and Gaussian noise. The work is organized in four steps as follows: (1) image is denoised by filtering method, (2) image is denoised by wavelet based techniques using thresholding, (3) hard thresholding and filtering method applied simultaneously on noisy image, (4) results of PSNR (peak signal to noise ratio) and MSE (mean square error) are calculated by comparing all cases.     

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.     

Cascaded and Recursive ConvNets (CRCNN): An effective and flexible approach for image denoising

Recently, discriminative learning methods have gained substantial interest in solving inverse imaging problems due to their decent performance and fast inferencing capability. Those methods need separate models for specific noise levels, which in turn require multiple models to be trained to denoise an image. However, images exhibit spatial variant noise which limits the applicability of such methods. In addition, the discriminative learning methods introduce artifacts such as blurring, deblocking, and so forth while denoising an image. To address these issues, we propose a cascaded and recursive convolutional neural network (CRCNN) framework which can cope with spatial variant noise and blur artifacts in a single denoising framework. The CRCNN takes into account down-sampled sub-images for fast inferencing along with the noise level map. We adopt the hybrid orthogonal projection and estimation method on the convolutional layers to improve the generalization capability of the network in terms of non-uniform and spatial variant noise levels. In contrast to the existing methods, the CRCNN framework allows both denoising and deblurring of images using a single framework which preserves the fine details in a denoised image. Extensive experiments have been conducted to validate the effectiveness and flexibility of the CRCNN framework on real as well as synthetic noisy images in comparison to the state-of-the-art denoising methods. The results show that the CRCNN performs effectively on both synthetic as well as spatial variant noise-induced images, thus, proving the practicability of the framework.     

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.     

一种非开关型快速随机脉冲噪声降噪算法

为提高现有开关型随机脉冲噪声（Random-Valued Impulse Noise,RVIN）降噪算法的降噪性能,提出了一种基于卷积神经网络的非开关型RVIN快速降噪算法（Fast Non-switching RVIN Denoising Algorithm,FNRDA）.首先,利用噪声检测器随机地检测给定噪声图像中少量不同位置处的像素点;然后,将检测为RVIN噪声点的个数除以被检像素点总数转化为噪声比例值;最后,根据噪声比例值调用相应预先训练好的非开关型卷积神经网络降噪模型,快速且高质量地完成图像降噪任务.实验结果表明：所提出的非开关型FNRDA算法在各噪声比例下的综合性能（降噪效果和执行效率）优于经典的开关型RVIN降噪算法,适用于图像恢复、信号检测、无线通讯等实时系统中.     

基于加权自适应方向提升小波的图像去噪研究

本文介绍了一种基于加权自适应方向提升小波(WADL,Weighted adaptive directional lifting)和普通提升方法相结合的图像去噪方法,此方法能够较好地对噪声进行抑制,同时保护图像的纹理边缘较少受到损失。在仿真试验中我们通过对噪声图像进行分类,对属于纹理密集区域采用WADL方法去噪,对平滑区域采用普通提升去噪,得到了比较好的去噪结果。     

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.     

基于分数阶图像增强的P-M模型

P-M扩散模型是图像处理中用于去噪平滑的经典模型,但在实际应用中常会出现零散的斑点。为了去除残存的噪点,通常采用平滑处理来消除高梯度的噪声,但这又模糊了边缘,损失了细节信息。从此问题入手,采用在噪声图像平滑处理后,应用分数阶微分来锐化图像,由于分数阶微分的非线性特性,此方法可以在增强边缘特征的同时不明显加强噪声信息。实验证明,通过文中方法的处理,图像质量和信噪比都有了明显提升。     

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.     

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.     

三维医学图像的混合噪声去除方法

针对医学图像在采集传输等过程中易受噪声污染,且目前多数去噪方法对混合噪声去噪效果不好,影响三维重构精度的问题,提出了基于自适应三维分数阶积分和中值滤波结合的混合噪声去除方法。首先介绍了几种传统方法在去除混合噪声中的不足,然后基于三维图像梯度信息提出了三维分数阶积分的自适应分数阶阶数,利用分数阶积分和中值滤波的各自优点,将两者结合对混合噪声去噪,并提出了基于混合去噪的边缘曲面追踪算法。实验结果和数据分析表明,提出的混合去噪方法能够从噪声污染的医学图像切片中追踪出高精度边缘曲面,与传统去噪方法相比,具有更好的去噪效果。     

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.     

基于尺度乘积和相关性的图像去噪

为了去除图像的噪声,提出了一种基于尺度乘积和尺度相关性的平稳小波交换图像去噪方法.在传统小波系数估计的基础上,考虑到尺度间的相关性,利用不同尺度小波系数形成的系数向量,通过线性最小均方误差估计小波系数,获得各个高频子带的估计系数.针对单纯利用尺度间相关性去噪造成的图像边缘失真问题,在不同尺度小波系数形成的系数向量中引入了小波系数乘积,不但可以较好区分边缘信息和噪声信息,而且提高了原有算法的去噪能力.仿真结果表明,该图像去噪算法能有效去除图像噪声,较好保持图像边缘,在峰值信噪比和视觉质量上都有较大提高.     

基于专家场先验模型的图像超分辨重建算法

为了进一步提高图像超分辨率重建的质量,针对非局部集中稀疏表示算法中重建图像的噪声问题,提出了一种基于专家场先验模型的图像超分辨率重建改进算法。首先,利用专家场模型从图像训练集中学习整幅图像的先验知识建立全局先验模型;然后将学习到的先验信息用于非局部集中稀疏表示模型求解最优稀疏表示系数;最后,得到高分辨率图像估计。该算法在超分辨率重建迭代运算的同时,同步更新专家场模型参数,因此在不显著增加运算复杂度的情况下,通过选取合适的先验约束,有效地增强了图像重建的效果。实验结果表明:相比非局部集中稀疏表示算法,文中算法对无噪和有噪降质图像均能取得较好的峰值信噪比结果,并且能够进一步提高有噪图像的去噪效果。     

A Robust Hidden Markov Gauss Mixture Vector Quantizer for a Noisy Source

Noise is ubiquitous in real life and changes image acquisition, communication, and processing characteristics in an uncontrolled manner. Gaussian noise and Salt and Pepper noise, in particular, are prevalent in noisy communication channels, camera and scanner sensors, and medical MRI images. It is not unusual for highly sophisticated image processing algorithms developed for clean images to malfunction when used on noisy images. For example, hidden Markov Gauss mixture models (HMGMM) have been shown to perform well in image segmentation applications, but they are quite sensitive to image noise. We propose a modified HMGMM procedure specifically designed to improve performance in the presence of noise. The key feature of the proposed procedure is the adjustment of covariance matrices in Gauss mixture vector quantizer codebooks to minimize an overall minimum discrimination information distortion (MDI). In adjusting covariance matrices, we expand or shrink their elements based on the noisy image. While most results reported in the literature assume a particular noise type, we propose a framework without assuming particular noise characteristics. Without denoising the corrupted source, we apply our method directly to the segmentation of noisy sources. We apply the proposed procedure to the segmentation of aerial images with Salt and Pepper noise and with independent Gaussian noise, and we compare our results with those of the median filter restoration method and the blind deconvolution-based method, respectively. We show that our procedure has better performance than image restoration-based techniques and closely matches to the performance of HMGMM for clean images in terms of both visual segmentation results and error rate.