Denoising 3D MR images by the enhanced non-local means filter for Rician noise

The non-local means (NLM) filter removes noise by calculating the weighted average of the pixels in the global area and shows superiority over existing local filter methods that only consider local neighbor pixels. This filter has been successfully extended from 2D images to 3D images and has been applied to denoising 3D magnetic resonance (MR) images. In this article, a novel filter based on the NLM filter is proposed to improve the denoising effect. Considering the characteristics of Rician noise in the MR images, denoising by the NLM filter is first performed on the squared magnitude images. Then, unbiased correcting is carried out to eliminate the biased deviation. When performing the NLM filter, the weight is calculated based on the Gaussian-filtered image to reduce the disturbance of the noise. The performance of this filter is evaluated by carrying out a qualitative and quantitative comparison of this method with three other filters, namely, the original NLM filter, the unbiased NLM (UNLM) filter and the Rician NLM (RNLM) filter. Experimental results demonstrate that the proposed filter achieves better denoising performance over the other filters being compared.     

Generalized total variation-based MRI Rician denoising model with spatially adaptive regularization parameters

Magnetic resonance imaging (MRI) is an outstanding medical imaging modality but the quality often suffers from noise pollution during image acquisition and transmission. The purpose of this study is to enhance image quality using feature-preserving denoising method. In current literature, most existing MRI denoising methods did not simultaneously take the global image prior and local image features into account. The denoising method proposed in this paper is implemented based on an assumption of spatially varying Rician noise map. A two-step wavelet-domain estimation method is developed to extract the noise map. Following a Bayesian modeling approach, a generalized total variation-based MRI denoising model is proposed based on global hyper-Laplacian prior and Rician noise assumption. The proposed model has the properties of backward diffusion in local normal directions and forward diffusion in local tangent directions. To further improve the denoising performance, a local variance estimator-based method is introduced to calculate the spatially adaptive regularization parameters related to local image features and spatially varying noise map. The main benefit of the proposed method is that it takes full advantage of the global MR image prior and local image features. Numerous experiments have been conducted on both synthetic and real MR data sets to compare our proposed model with some state-of-the-art denoising methods. The experimental results have demonstrated the superior performance of our proposed model in terms of quantitative and qualitative image quality evaluations.     

A general strategy for anisotropic diffusion in MR image denoising and enhancement

Anisotropic diffusion (AD) has proven to be very effective in the denoising of magnetic resonance (MR) images. The result of AD filtering is highly dependent on several parameters, especially the conductance parameter. However, there is no automatic method to select the optimal parameter values. This paper presents a general strategy for AD filtering of MR images using an automatic parameter selection method. The basic idea is to estimate the parameters through an optimization step on a synthetic image model, which is different from traditional analytical methods. This approach can be easily applied to more sophisticated diffusion models for better denoising results. We conducted a systematic study of parameter selection for the AD filter, including the dynamic parameter decreasing rate, the parameter selection range for different noise levels and the influence of the image contrast on parameter selection. The proposed approach was validated using both simulated and real MR images. The model image generated using our approach was shown to be highly suitable for the purpose of parameter optimization. The results confirm that our method outperforms most state-of-the-art methods in both quantitative measurement and visual evaluation. By testing on real images with different noise levels, we demonstrated that our method is sufficiently general to be applied to a variety of MR images.     

Laplacian based non-local means denoising of MR images with Rician noise

Magnetic Resonance (MR) image is often corrupted with a complex white Gaussian noise (Rician noise) which is signal dependent. Considering the special characteristics of Rician noise, we carry out nonlocal means denoising on squared magnitude images and compensate the introduced bias. In this paper, we propose an algorithm which not only preserves the edges and fine structures but also performs efficient denoising. For this purpose we have used a Laplacian of Gaussian (LoG) filter in conjunction with a nonlocal means filter (NLM). Further, to enhance the edges and to accelerate the filtering process, only a few similar patches have been preselected on the basis of closeness in edge and inverted mean values. Experiments have been conducted on both simulated and clinical data sets. The qualitative and quantitative measures demonstrate the efficacy of the proposed method.     

Rician noise reduction in magnetic resonance images using adaptive non-local mean and guided image filtering

This paper proposes a Rician noise reduction method for magnetic resonance (MR) images. The proposed method is based on adaptive non-local mean and guided image filtering techniques. In the first phase, a guidance image is obtained from the noisy image through an adaptive non-local mean filter. Sobel operators are applied to compute the strength of edges which is further used to control the spread of the kernel in non-local mean filtering. In the second phase, the noisy and the guidance images are provided to the guided image filter as input to restore the noise-free image. The improved performance of the proposed method is investigated using the simulated and real data sets of MR images. Its performance is also compared with the previously proposed state-of-the art methods. Comparative analysis demonstrates the superiority of the proposed scheme over the existing approaches.     

Blind Additive Gaussian White Noise Level Estimation from a Single Image by Employing Chi-Square Distribution

The additive Gaussian white noise (AGWN) level in real-life images is usually unknown, for which the empirical setting will make the denoising methods over-smooth fine structures or remove noise incompletely. The previous noise level estimation methods are easily lost in accurately estimating them from images with complicated structures. To cope with this issue, we propose a novel noise level estimation scheme based on Chi-square distribution, including the following key points: First, a degraded image is divided into many image patches through a sliding window. Then, flat patches are selected by using a patch selection strategy on the gradient maps of those image patches. Next, the initial noise level is calculated by employing Chi-square distribution on the selected flat patches. Finally, the stable noise level is optimized by an iterative strategy. Quantitative, with association, to qualitative results of experiments on synthetic real-life images validate that the proposed noise level estimation method is effective and even superior to the state-of-the-art methods. Extensive experiments on noise removal using BM3D further illustrate that the proposed noise level estimation method is more beneficial for achieving favorable denoising performance with detail preservation.     

Nonlocal maximum likelihood estimation method for denoising multiple-coil magnetic resonance images

Effective denoising is vital for proper analysis and accurate quantitative measurements from magnetic resonance (MR) images. Even though many methods were proposed to denoise MR images, only few deal with the estimation of true signal from MR images acquired with phased-array coils. If the magnitude data from phased array coils are reconstructed as the root sum of squares, in the absence of noise correlations and subsampling, the data is assumed to follow a non central-χ distribution. However, when the k-space is subsampled to increase the acquisition speed (as in GRAPPA like methods), noise becomes spatially varying. In this note, we propose a method to denoise multiple-coil acquired MR images. Both the non central-χ distribution and the spatially varying nature of the noise is taken into account in the proposed method. Experiments were conducted on both simulated and real data sets to validate and to demonstrate the effectiveness of the proposed method.     

采用非局部主成分分析的极大似然估计图像去噪

本文提出一种采用非局部主成分分析的极大似然估计去噪方法.首先采用非局部主成分分析算法来计算像素邻域间的灰度值和纹理结构相似性,然后通过极大似然估计方法估计最优复原图像.本方法使用非局部主成分分析克服现有局部性去噪方法模糊边界等缺陷,引入极大似然估计方法来改进现有非局部均值的简单加权均值去噪处理,从而提高对图像细节信息的复原能力.最后分别使用本文方法、非局部均值和局部极大似然估计三种去噪方法,在不同噪音大小和不同几何纹理复杂度的图像中进行定性和定量的去噪实验.结果表明,本文方法可在保持图像细节和纹理信息的情况下有效去噪,较之现有方法效果更好.     

去除乘性噪音的主成分分析算法

雷达成像系统的进一步应用依赖于对图像中噪音的有效抑制.在目前现有消除噪音方法的基础上,基于图像的局部相似性,结合主成分分析法,提出一种新的有效去除乘性噪音的滤波算法.乘性噪音经对数变换后可转化为加性噪音处理.分析了对数域中噪音的类型.首先在图像的对数域,通过非局部方法选取局部相似块作为训练样本,利用主成分分析法提取出信号的主要特征.然后基于统计理论中最小均方误差估计法给出了一种适用于图像信息的阈值原则.最后分析了变换过程引起的偏差,由对数域的偏估计得到滤波图像.数值实验验证了新算法的有效性.对比于目前提出的变分方法,新算法处理后的图像有更高的信噪比和更好的视觉效果,且具有一定的实用性.     

用于MR图像非局域均值去噪的边缘增强策略

非局域均值(NLM)滤波有很好的去噪效果并已成功地应用于磁共振图像的去噪中,但与所有去噪方法相同,总是会在一定程度上模糊图像细节. 该文提出将从原始图像中提取出来的高频信息与NLM去噪图像相融合,来还原在去噪过程中丢失的细节. 首先利用一种基于拉普拉斯金字塔的多分辨率方法,从原始图像中提取出包含丰富的边缘信息的高频组分. 然后利用作者提出的一种新的基于SUSAN算子的边缘检测算子产生一幅连续的边缘图,并利用该边缘图将高频组分与NLM方法去噪的图像相融合. 该方法在图像的平滑区域取得了良好的去噪效果,同时可以保留甚至增强图像的细节. 同时,该方法对图像的增强不会导致增强图像中常见的伪影.     

Superiority of 3D wavelet-packet denoising in MR microscopy

Three dimensional Magnetic Resonance Imaging (MRI) datasets are becoming increasingly important in clinical and research applications because of their inherent signal to noise (SNR) advantages, high resolution and isotropic voxels. Despite SNR advantages, some 3D acquisitions may be SNR-limited, particularly in MR microscopy. Historically, both classic filtering and wavelet-based denoising techniques have been performed on a slice-by-slice basis. In principle, adaptive techniques such as best- basis wavelet-packet denoising might offer inherent advantages when performed in 3D, instead of 2D, by tracking through plane "structure" and suppressing noise "pseudostructure." This hypothesis was tested in 10 volumetric MR microscopy datasets from several different MR microscopy atlas projects. 3D wavelet-packet denoised images consistently yielded lower minimum mean-square error and subjectively perceived noise power than corresponding 2D denoised images using otherwise identical algorithms and parameters. MR microscopy researchers preferred the denoised images to the unprocessed images for their atlas projects.     

Complex denoising of MR data via wavelet analysis: application for functional MRI

A fast post-processing method for noise reduction of MR images, termed complex-denoising, is presented. The method is based on shrinking noisy discrete wavelet transform coefficients via thresholding, and it can be used for any MRI data-set with no need for high power computers. Unlike previous wavelet application to MR images, the denoising algorithm is applied, separately, to the two orthogonal sets of the complex MR image. The norm of the combined data are used to construct the image. With this method, signal-noise decoupling and Gaussian white noise assumptions used in the wavelet noise suppression scheme, are better fulfilled. The performance of the method is tested by carrying out a qualitative and quantitative comparison of a single-average image, complex-denoised image, multiple-average images, and a magnitude-denoised image, of a standard phantom. The comparison shows that the complex-denoising scheme improves the signal-to-noise and contrast-to-noise ratios more than the magnitude-denoising scheme, particularly in low SNR regions. To demonstrate the method strength, it is applied to fMRI data of somatosensory rat stimulation. It is shown that the activation area in a cross-correlation analysis is approximately 63% larger in the complex-denoised versus original data sets when equal threshold value is used. Application of the method of Principal Component Analysis to the complex-denoised, magnitude-denoised, and original data sets results in a similar but higher variance of the first few principal components obtained from the former data set as compared to those obtained from the later two sets.     

基于双边滤波算子的医学脊椎去噪

为了有效滤除医学脊椎模型的噪声点,同时更好地保持模型细节,提出了一种基于双边滤波算子的医学脊椎去噪模型.采用双边滤波在多尺度条件下进行脊椎三维模型轮廓线的提取,设计改进自适应扩散系数,以更好的优化控制整个扩散过程.根据图像的离散特征,建立相应的离散迭代方程,使迭代过程离散化,并设计迭代停止准则,当去噪平滑后的图像模型与噪声相关性最小时停止迭代.与经典的向异性扩散模型方法实验结果相比,本方法在解决去噪方面达到了很好的滤波效果,同时也较好地保持了医学图像的边缘细节特征,大大优于传统滤波算法.     

A novel denoising method based on Radon transform and filtered back-projection reconstruction algorithm

A novel denoising method based on Radon transform and filtered back-projection (FBP) image reconstruction algorithm was proposed. This method can be considered as a special mean filter on projection line, which is different from most of the traditional filters operated on adjacent templates that could bring serious blurs to images. The details of images processed by the proposed method can be preserved relatively complete and the denoising effect is satisfactory. To verify the denoising effect of the proposed method, the simulation was designed and carried out, and the image evaluation parameters were applied to analyze the denoising effect and the detail-preserving ability quantitatively. For further understanding of the proposed method, the basic denoising principle of this method was analyzed. Noise points and information points can be distinguished: the attenuation velocity of gray scale of noise points is faster than that of information points, which was verified by the experiment. The results of different parameters in the proposed method were compared and analyzed. Several kinds of traditional filters were compared with the proposed method, and the result shows that the proposed method is better than the traditional filters in the aspects of both denoising effect and detail-preserving ability. Apart from this, the proposed method is not particular about the kind of noise; therefore, it is a powerful method to deal with atypical noise, uncertain noise, and mixed noises.     

基于工业CT图像重构的网格模型的全局优化方法

针对用工业CT切片图像直接重构得到的网格模型质量不高的问题,提出一种不受拓扑结构限制的隐式曲面重构全局优化方法。该方法将三维表面模型用隐式函数来表示,通过模型提供的点云信息计算出隐式函数,提取等值面,实现曲面重构。针对隐式曲面重构数据处理量大的问题,引入FFTW快速傅里叶变换来提高效率。实验结果表明,该方法能够同时实现三角网格模型的去噪、网格平滑、简化以及孔洞修补,与保特征的均匀化网格平滑算法相比,去噪效果更好,效率更高。     

Low-field magnetic resonance imaging using multiplicative regularization

In this paper we present a magnetic resonance imaging (MRI) technique that is based on multiplicative regularization. Instead of adding a regularizing objective function to a data fidelity term, we multiply by such a regularizing function. By following this approach, no regularization parameter needs to be determined for each new data set that is acquired. Reconstructions are obtained by iteratively updating the images using short-term conjugate gradient-type update formulas and Polak-Ribière update directions. We show that the algorithm can be used as an image reconstruction algorithm and as a denoising algorithm. We illustrate the performance of the algorithm on two-dimensional simulated low-field MR data that is corrupted by noise and on three-dimensional measured data obtained from a low-field MR scanner. Our reconstruction results show that the algorithm effectively suppresses noise and produces accurate reconstructions even for low-field MR signals with a low signal-to-noise ratio.     

A weighted least squares algorithm for time-of-flight depth image denoising

In this paper, we present a new denoising method for the depth image of a time-of-flight (ToF) camera, based on weighted least squares (WLS) framework. The common method for ToF depth image denoising is to use bilateral filter. However, the ability of bilateral filter in edge preservation would be reduced while we attempt to smooth out larger spatial scale noise. In order to avoid this problem and preserve the edge information as much as possible, we introduce a new way to construct edge-preserving ToF depth image denoising based on WLS. We are to our knowledge the first to present a WLS-based method for ToF depth image denoising. Experimental results demonstrate that compared with bilateral filter, our proposed algorithm not only achieves better performance in edge preservation, but also improves the PSNR values of the denoised images by 0.5–2.6 dB.     

Non-local means algorithm with adaptive patch size and bandwidth

Non-local means algorithm is an effective denoising method that consists in some kind of averaging process carried on similar patches in a noisy image. Some internal parameters, such as patch size and bandwidth, strongly influence the performance of non-local means, but with the difficulty of tuning. Many solutions for choosing these two parameters, like cross-validation and Steins unbiased risk estimate criterion, are successful but computationally heavy. In this paper, we introduce a new feature metric that is capable of providing a quantitative measure of geometric structures of image in the presence of noise. The proposed region-based non-local means method first classifies a noisy image into several regions. Then, a local window and a local bandwidth value are selected pixel-wisely according to the property of each region and the local value of the new feature metric. Experiments on standard test images show that the proposed method outperforms the original non-local means version by around 1.34 dB and is comparable to or better than the performance of the current state-of-the-art non-local means based denoising algorithms, both visually and quantitatively.     

消除水下激光图像混合噪音的软形态滤波算法

除了采用距离选通等特殊机制来消除后向散射之外,水下激光成像系统作用距离的进一步提升依赖于对图像中噪音的有效抑制.在分析水下激光距离选通图像噪音特性的基础上,引入软形态学,设计了多方向结构元和极化软形态变换,组成开-闲级联滤波器.对于其中的重复度参量,以散斑指数和边缘能量为目标,采用离散差分算法优化.实验结果表明,该算法...     

高光谱遥感图像微分域三维混合去噪方法

高光谱遥感图像是一种三维数据,由二维空间信息和一维光谱信息组成。普通的对二维静态图像或一维光谱信息去噪的算法忽视了高光谱图像强烈的谱间相关性和图谱合一的特点,无法取得令人满意的效果。同时现代的高光谱遥感图像噪声级别相对较低,噪声方差随波段不同而不同。针对以上特点,提出一种微分域三维混合去噪方法。首先将高光谱遥感图像变换到光谱微分域,使细微的噪声变得显著。然后在微分域中,对二维空间域采用基于小波的非线性阈值去噪BayesShrink算法。为克服噪声方差不同的特点,对光谱维不再采用小波阈值去噪方法,而采用Savitzky-Golay滤波进行平滑。最后对微分域去噪平滑处理后的图像进行光谱积分,并进行积分修正,消除光谱积分中引入的积累误差。对信噪比为600∶1的机载可见红外成像光谱仪数据(AVIRIS)实验表明,该算法能有效地降低噪声,将信噪比提高到2 000∶1以上。