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.     

Wavelet domain de-noising of time-courses in MR image sequences

Magnetic resonance images acquired with high temporal resolution often exhibit large noise artifacts, which arise from physiological sources as well as from the acquisition hardware. These artifacts can be detrimental to the quality and interpretation of the time-course data in functional MRI studies. A class of wavelet-domain de-noising algorithms estimates the underlying, noise-free signal by thresholding (or 'shrinking') the wavelet coefficients, assuming the underlying temporal noise of each pixel is uncorrelated and Gaussian. A Wiener-type shrinkage algorithm is developed in this paper, for de-noising either complex- or magnitude-valued image data sequences. Using the de-correlation properties of the wavelet transform, as elucidated by Johnstone and Silverman, the assumption of i.i.d. Gaussian noise can be abandoned, opening up the possibility of removing colored noise. Both wavelet- and wavelet-packet based algorithms are developed, and the Wiener method is compared to the traditional Hard and Soft wavelet thresholding methods of Donoho and Johnstone. The methods are applied to two types of data sets. In the first, an artificial set of complex-valued images was constructed, in which each pixel has a simulated bimodal time-course. Gaussian noise was added to each of the real and imaginary channels, and the noise removed from the complex image sequence as well as the magnitude image sequence (where the noise is Rician). The bias and variance between the original and restored paradigms was estimated for each method. It was found that the Wiener method gives better balance in bias and variance than either Hard or Soft methods. Furthermore, de-noising magnitude data provides comparable accuracy of the restored images to that obtained from de-noising complex data. In the second data set, an actual in vivo complex image sequence containing unknown physiological and instrumental noise was used. The same bimodal paradigm as in the first data set was added to pixels in a small localized region of interest. For the paradigm investigated here, the smooth Daubechies wavelets provide better de-noising characteristics than the discontinuous Haar wavelets. Also, it was found that wavelet packet de-noising offers no significant improvement over the computationally more efficient wavelet de-noising methods. For the in vivo data, it is desirable that the groups of "activated" time-courses are homogeneous. It was found that the internal homogeneity of the group of time-courses increases when de-noising is applied. This suggests using de-noising as a pre-processing tool for both exploratory and inferential data analysis methods in fMRI.     

基于神经网络和小波变换的MRI图像去噪方法

过去10年中,小波变换在图像去噪中取得了很大的成功.人们提出了多种适用于小波去噪的阈值方法,而这些方法就是希望能够正确地反映有噪声小波系数与无噪声小波系数之间的映射关系.基于这种想法,我们提出一种在小波域中利用神经网络寻找这种映射关系的图像去噪新方法.我们把该方法应用于不同噪声分布的磁共振图像的去噪,取得了良好的效果.     

A wavelet-based method for improving signal-to-noise ratio and contrast in MR images

Magnetic resonance (MR) images acquired with fast measurement often display poor signal-to-noise ratio (SNR) and contrast. With the advent of high temporal resolution imaging, there is a growing need to remove these noise artifacts. The noise in magnitude MR images is signal-dependent (Rician), whereas most de-noising algorithms assume additive Gaussian (white) noise. However, the Rician distribution only looks Gaussian at high SNR. Some recent work by Nowak employs a wavelet-based method for de-noising the square magnitude images, and explicitly takes into account the Rician nature of the noise distribution. In this article, we apply a wavelet de-noising algorithm directly to the complex image obtained as the Fourier transform of the raw k-space two-channel (real and imaginary) data. By retaining the complex image, we are able to de-noise not only magnitude images but also phase images. A multiscale (complex) wavelet-domain Wiener-type filter is derived. The algorithm preserves edges better when the Haar wavelet rather than smoother wavelets, such as those of Daubechies, are used. The algorithm was tested on a simulated image to which various levels of noise were added, on several EPI image sequences, each of different SNR, and on a pair of low SNR MR micro-images acquired using gradient echo and spin echo sequences. For the simulated data, the original image could be well recovered even for high values of noise (SNR approximately 0 dB), suggesting that the present algorithm may provide better recovery of the contrast than Nowak's method. The mean-square error, bias, and variance are computed for the simulated images. Over a range of amounts of added noise, the present method is shown to give smaller bias than when using a soft threshold, and smaller variance than a hard threshold; in general, it provides a better bias-variance balance than either hard or soft threshold methods. For the EPI (MR) images, contrast improvements of up to 8% (for SNR = 33 dB) were found. In general, the improvement in contrast was greater the lower the original SNR, for example, up to 50% contrast improvement for SNR of about 20 dB in micro-imaging. Applications of the algorithm to the segmentation of medical images, to micro-imaging and angiography (where the correct preservation of phase is important for flow encoding to be possible), as well as to de-noising time series of functional MR images, are discussed.     

基于小波域的维纳滤波算法在锥束牙科CT中的应用

提出一种小波域的维纳滤波方法对锥束牙科CT断层图像进行降噪。该算法以db4小波作为分解小波对CT图像进行分解,在分解后的每个子带再进行维纳滤波,并根据图像的区域统计特性对每个子带的局部均值和噪声方差估计参数进行了调整。利用降噪后的小波系数重构图像,得到降噪后的CT断层图像。通过计算机仿真及锥束牙科CT的真实数据测试表明,本文采用的方法有效抑制了图像噪声,提高了图像的信噪比,明显改善了图像的视觉效果。     

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.     

The influence of the resolution and contrast on measuring the articular cartilage volume in magnetic resonance images

The progression of OA in patients may be followed by measuring the volume of articular cartilage from MR images. We attempted to determine the reproducibility of volume measurements of articular cartilage made from magnetic resonance images of the knees and the dependence of the reproducibility on image resolution and contrast-to-noise. A fat-suppressed 3D technique was used to generate four image sets with different image resolution. Each patient was imaged twice to obtain image pairs at each resolution. To assess the dependence of reproducibility on noise we generated six image sets for each patient by adding noise to the original images and repeating the comparison. On each image set, the femoral, tibial, and patellar cartilage were outlined by a combination of computer and manual methods, and the images were used to calculate the volume of each cartilage plate. Comparing the coefficient of variance between the volume measurements made from the two visits, the volume measurements made from images with the highest resolution (0.275 x 0.275 x 1.0 mm) had the highest reproducibility. The high resolution images of the tibia and femur had the least partial-volume averaging and, as a result, better defined the boundaries between cartilage and adjacent tissues. A different trend was evident for the patella. For studies of osteoarthritis therapies, we recommend using MR images with the highest possible in-plane spatial resolution to provide the most reproducible volume measurements of knee cartilage.     

An effective noise removal technique for recovering the shapes of diamond abrasive grains in SLM images degraded by clustered spike noise

A new noise-removal technique is applied to scanning laser microscopic (SLM) images to remove clustered spike noise in the images and to recover the shapes of diamond abrasive grains degraded by the noise. For achievement of this purpose, noise points in the SLM image are accurately detected by taking advantage of their properties in the space and spatial-frequency regions. The noise points are removed by a method of smoothing that is based on linear interpolation; that is, their pixel values are replaced by the interpolated values of their non-noise neighboring points. Noise-point information in the space region is acquired from image segmentation based on pixel classification, while noise-point information in the frequency region is derived from redundant wavelet decomposition for the SLM image. Fisher's linear discriminant method is used to yield the two noise-point images. The degraded grain shapes in the SLM images at different noise levels are satisfactorily recovered with a single iteration of smoothing without losses in sharp edges although a single smoothing needed four interpolations. Thus, the present noise-removal technique is shown to be effective for recovering the original shapes of the grains in every SLM image.     

基于梯度和小波变换的水下距离选通图像去噪

水体的散射效应、激光光斑、成像器件的非理想化等因素使得图像出现大量无规律粒状噪声,它们增加了水下距离选通图像的背景噪声,模糊了目标轮廓,掩盖了目标细节,降低了图像的信噪比。针对上述问题本文提出了一种基于梯度和小波变换的去噪方法。首先对图像进行余弦小波变换,得到不同频率空间的图像集。低频空间引入新的图像梯度强化方法以提高图像的纹理信息量;对应非均匀性条带的LH或HL空间做曲面拟合处理以消除非均匀性条带的影响;在HH空间去噪过程中,低层空间做非局部均值处理以保留图像相似信息,高层空间做分数阶积分处理以保留图像细节信息。最后小波逆变换得到结果图像。从实验水槽中采集水下图像进行算法验证,将改进方法与已有算法比对分析。实验表明,本文所研究的水下去噪算法,能够平滑噪声且更大限度地保留图像细节纹理,在客观评价指标上提升了6%。     

Multispectral MR images segmentation based on fuzzy knowledge and modified seeded region growing

Magnetic resonance imaging (MRI) is a valuable diagnostic tool in medical science due to its capability for soft-tissue characterization and three-dimensional visualization. One potential application of MRI in clinical practice is brain parenchyma classification and segmentation. Based on fuzzy knowledge and modified seeded region growing, this work proposes a novel image segmentation method, called Fuzzy Knowledge-Based Seeded Region Growing (FKSRG), for multispectral MR images. In this work, fuzzy knowledge includes the fuzzy edge, fuzzy similarity and fuzzy distance, which are obtained from relationships between pixels in multispectral MR images and are applied to the modified seeded regions growing process. In conventional regions merging, the final number of regions is unknown. Therefore, a Target Generation Process is proposed and applied to support conventional regions merging, such that the FKSRG method does not over- or undersegment images. Finally, two image sets, namely, computer-generated phantom images and real MR images, are used in experiments to assess the effectiveness of the proposed FKSRG method. Experimental results demonstrate that the FKSRG method segments multispectral MR images much more effectively than the Functional MRI of the Brain Automated Segmentation Tool, K-means and Support Vector Machine methods.     

基于二代curvelet变换的图像融合研究

曲波(Curvelet)作为一种新的多尺度分析方法比小波更加适合分析二维图像中的曲线或直线状边缘特征,而且具有更高的逼近精度和更好的稀疏表达能力.将curvelet变换引入图像融合,能够更好地提取原始图像的特征,为融合图像提供更多的信息.第二代curvelet理论的提出也使得其理论更易理解和实现.因此,提出了一种基于第二代curvelet变换的图像融合方法,首先将图像进行curvelet变换,然后在相应尺度上利用融合规则将curvelet系数融合,最后进行重构得到融合结果.对多聚焦图像进行了实验,采用均方误差、偏差指数和相关系数对融合结果进行了客观评价,并与基于小波变换的融合进行了比较,实验结果表明该方法除分解2层时与小波性能相当,取其他分解层数时均获得更好的融合效果.     

Image fusion scheme using a novel dual-channel PCNN in lifting stationary wavelet domain

This paper presents a new multi-source image fusion scheme based on lifting stationary wavelet transform (LSWT) and a novel dual-channel pulse-coupled neural network (PCNN). By using LSWT, we can calculate a flexible multiscale and shift-invariant representation of registered images. After decomposing the original images using LSWT, a new dual-channel pulse coupled neural network, which can overcome some shortcomings of original PCNN for image fusion and putout the fusion image directly, is proposed and used for the fusion of sub-band coefficients of LSWT. In this fusion scheme, a new sum-modified-laplacian(NSML) of the low frequency sub-band image, which represent the edge-feature of the low frequency sub-band image in SLWT domain, is presented and input to motivate the dual-channel PCNN. For the fusion of high frequency sub-band coefficients, a novel local neighborhood modified-laplacian (LNML) measurement is developed and used as external stimulus to motivate the dual-channel PCNN. This fusion scheme is verified on several sets of multi-source images, and the experiments show that the algorithms proposed in the paper can significantly improve image fusion performance, compared with the fusion algorithms such as traditional wavelet, LSWT, and LSWT-PCNN in terms of objective criteria and visual appearance.     

一种照明无关的小波多尺度相乘边缘检测方法

提出了一种照明无关的小波多尺度相乘边缘检测方法,用于从非均匀的弱照明图像中提取边缘。根据照明反射图像形成模板与CCD相机成像原理,推导出图像的对应小波变换公式。然后,对图像局部区域中噪声、边缘与背景像素的小波系数进行比较分析,设计了一种照明无关的小波边缘检测公式。为增强边缘并抑制噪声,提出了一种改善的小波多尺度相乘边缘检测方法,并依照小波变换后边缘像素的特征,提取单像素的边缘。采用仿真和真实的非均匀的弱照明图像对该边缘检测算法进行验证,并与另外两种边缘检测方法进行定性的和定量的比较。实验结果证实了这种边缘检测方法能够从灰度不均匀的低衬比度图像中正确有效地提取边缘。     

一种基于小波变换的红外偏振融合算法

针对红外偏振图像可以较好地抑制背景噪声,对目标边缘信息比较敏感的特点,提出一种基于小波变换的红外偏振融合算法,它主要用于红外辐射强度图像和偏振度图像融合,增加图像的信息量。首先采用小波变换对参与融合的每幅图像分别进行各尺度分解,得到各尺度小波系数,然后针对不同尺度小波系数,采用邻域平均梯度为判据进行融合,得到融合后的各尺度小波系数,最后通过小波逆变换进行图像重构,得到融合图像。融合前后的图像对比表明融合图像在保留辐射强度图像的清晰度的同时,突出了目标的边缘、轮廓信息。相对于辐射强度图像,融合图像的梯度均值提高了112%,相对于偏振度图像,融合图像的标准差提高了151%,信息熵提高了38%。     

Image-fusion-based multi-resolution active contour model

This paper proposes an active contour model (snake) based on image fusion, which is used in object detection and object tracking. Firstly, a multi-resolution image fusion with wavelet transform is applied to obtain the multi-resolution fused images. Secondly, in the low-frequency sub-image, a snake is applied with the Sobel operator to detect the object's contour; and in other high-frequency sub-images, a wavelet-based snake is applied. The two convergent snakes are fused in a multi-resolution scheme to obtain a fused snake in the fused image in an original resolution. Experiment results indicate this fused snake's detection or tracking accuracy is improved greatly.     

基于中值预滤波的航空图像小波去噪算法研究

结合航空图像的噪声来源与图像特性,提出一种基于中值预滤波的图像小波去噪算法.图像首先经中值滤波器进行预滤波,滤除随机的脉冲式噪声,然后对处理后的图像进行小波变换,与给定阈值相比,对可明显判为信号或噪声的系数进行相应处理;对不确定为信号或噪声的系数进行多尺度上的相关性追溯,判别其归属后进行处理.实验结果表明:该方法客观上提高了图像的信噪比,主观上使去噪后的图像纹理分明,能更好地适合人眼的视觉特性,有利于航空图像的分析、判读.     

Exploiting the wavelet structure in compressed sensing MRI

Sparsity has been widely utilized in magnetic resonance imaging (MRI) to reduce k-space sampling. According to structured sparsity theories, fewer measurements are required for tree sparse data than the data only with standard sparsity. Intuitively, more accurate image reconstruction can be achieved with the same number of measurements by exploiting the wavelet tree structure in MRI. A novel algorithm is proposed in this article to reconstruct MR images from undersampled k-space data. In contrast to conventional compressed sensing MRI (CS-MRI) that only relies on the sparsity of MR images in wavelet or gradient domain, we exploit the wavelet tree structure to improve CS-MRI. This tree-based CS-MRI problem is decomposed into three simpler subproblems then each of the subproblems can be efficiently solved by an iterative scheme. Simulations and in vivo experiments demonstrate the significant improvement of the proposed method compared to conventional CS-MRI algorithms, and the feasibleness on MR data compared to existing tree-based imaging algorithms.     

基于粗糙集与小波变换的图像融合算法

粗糙集理论是处理不确定性问题的数学方法，本文提出了基于粗糙集与小波变换相结合的图像融合算法。该方法首先将粗糙集理论应用于图像滤波中，对含有椒盐噪声的图像进行粗糙中值滤波，然后对滤波后的图像进行小波融合。实验结果表明，粗糙中值滤波有较强的去噪能力，且较好地保持了图像的细节信息，在此基础上进行小波融合，使得融合结果图像具有良好的效果。     

基于粗糙集与小波反锐化掩模的图像增强

为了有效去除图像中的干扰噪音,改善模糊不清晰的有用边缘细节信息,提高图像的层次感和清晰度,提出将粗糙集和小波反锐化掩模相结合的方法来实现图像增强.运用粗糙集中的近似及等价属性关系将知识化后的图像划分成不同的区域,再根据估计好的阈值进行数据约简,实现有效去除噪音.运用小波反锐化掩模法对图像的轮廓及细节信息进行增强处理,完成图像的最终增强.实验结果表明,不论在主观的视觉效果上,还是客观的噪音均方误差,该方法的处理结果都是较为理想的.     

Double image encryption based on linear blend operation and random phase encoding in fractional Fourier domain

A novel method for double image encryption is proposed by using linear blend operation and double-random phase encoding (DRPE) in the fractional Fourier domain. In the linear blend operation, a random orthogonal matrix is defined to linearly recombined pixel values of two original images. The resultant blended images are employed to constitute a complex-valued image, which is encrypted into an encrypted image with stationary white distribution by the DRPE in the fractional Fourier domain. The primitive images can be exactly recovered by applying correct keys with fractional orders, random phase masks and random angle function that is used in linear blend operation. Numerical simulations demonstrate that the proposed scheme has considerably high security level and certain robustness against data loss and noise disturbance.