Post-processing noise removal algorithm for magnetic resonance imaging based on edge detection and wavelet analysis

A post-processing noise suppression technique for biomedical MRI images is presented. The described procedure recovers both sharp edges and smooth surfaces from a given noisy MRI image; it does not blur the edges and does not introduce spikes or other artefacts. The fine details of the image are also preserved. The proposed algorithm first extracts the edges from the original image and then performs noise reduction by using a wavelet de-noise method. After the application of the wavelet method, the edges are restored to the filtered image. The result is the original image with less noise, fine detail and sharp edges. Edge extraction is performed by using an algorithm based on Sobel operators. The wavelet de-noise method is based on the calculation of the correlation factor between wavelet coefficients belonging to different scales. The algorithm was tested on several MRI images and, as an example of its application, we report the results obtained from a spin echo (multi echo) MRI image of a human wrist collected with a low field experimental scanner (the signal-to-noise ratio, SNR, of the experimental image was 12). Other filtering operations have been performed after the addition of white noise on both channels of the experimental image, before the magnitude calculation. The results at SNR = 7, SNR = 5 and SNR = 3 are also reported. For SNR values between 5 and 12, the improvement in SNR was substantial and the fine details were preserved, the edges were not blurred and no spikes or other artefacts were evident, demonstrating the good performances of our method. At very low SNR (SNR = 3) our result is worse than that obtained by a simpler filtering procedure.     

一种基于模糊均差和小波变换的医学图像去噪方法

小波阈值萎缩法能够有效地去除图像中的噪声,去噪阈值直接影响去噪的效果,而噪声标准差在去噪阈值的确定中起着至关重要的作用。针对医学图像的特点、基于寻找更合适的噪声标准差估计方法,本研究提出了一种新的利用模糊均差代替普通标准方差估计噪声标准差的方法。在各层小波分解的低频图像中利用模糊积分估计噪声标准差,然后确定每一层去噪阈值,进行图像去噪。试验结果表明,本研究算法在去除噪声的同时也较好地保持了图像的细节。     

基于多层小波分解与稳定分布的超声图像散粒噪声抑制新方法

医学超声图像在应用中遇到的一个重要问题是如何消除图像中由于散射现象的相干本质而引起的多径乘性散粒噪声。对数超声图像的二维小波系数服从具有尖峰和拖尾的边缘分布的非高斯分布。α稳定分布可以用来描述这类重拖尾非高斯尖峰脉冲信号和噪声。本研究利用一种散粒噪声模型，通过对对数超声图像的多层小波分解的高频系数的分析与稳定分布建模，提出了一种新的基于闽值的二维小波分解系数的检测分类方法，得到一种基于多层小波分解与稳定分栉模型的超声图像散粒噪声的抑制新方法。仿真结果表明，该方法比传统的基于高斯假设下的阈值去噪方法性能更好。     

Wavelet-based de-noising algorithm for images acquired with parallel magnetic resonance imaging (MRI)

Wavelet-based de-noising has been shown to improve image signal-to-noise ratio in magnetic resonance imaging (MRI) while maintaining spatial resolution. Wavelet-based de-noising techniques typically implemented in MRI require that noise displays uniform spatial distribution. However, images acquired with parallel MRI have spatially varying noise levels. In this work, a new algorithm for filtering images with parallel MRI is presented. The proposed algorithm extracts the edges from the original image and then generates a noise map from the wavelet coefficients at finer scales. The noise map is zeroed at locations where edges have been detected and directional analysis is also used to calculate noise in regions of low-contrast edges that may not have been detected. The new methodology was applied on phantom and brain images and compared with other applicable de-noising techniques. The performance of the proposed algorithm was shown to be comparable with other techniques in central areas of the images, where noise levels are high. In addition, finer details and edges were maintained in peripheral areas, where noise levels are low. The proposed methodology is fully automated and can be applied on final reconstructed images without requiring sensitivity profiles or noise matrices of the receiver coils, therefore making it suitable for implementation in a clinical MRI setting.     

Robust non-homomorphic approach for speckle reduction in medical ultrasound images

Most existing wavelet-based image denoising techniques are developed for additive white Gaussian noise. In applications to speckle reduction in medical ultrasound (US) images, the traditional approach is first to perform the logarithmic transform (homomorphic processing) to convert the multiplicative speckle noise model to an additive one, and then the wavelet filtering is performed on the log-transformed image, followed by an exponential operation. However, this non-linear operation leads to biased estimation of the signal and increases the computational complexity of the filtering method. To overcome these drawbacks, an efficient, non-homomorphic technique for speckle reduction in medical US images is proposed. The method relies on the true characterisation of the marginal statistics of the signal and speckle wavelet coefficients. The speckle component was modelled using the generalised Nakagami distribution, which is versatile enough to model the speckle statistics under various scattering conditions of interest in medical US images. By combining this speckle model with the generalised Gaussian signal first, the Bayesian shrinkage functions were derived using the maximum a posteriori (MAP) criterion. The resulting Bayesian processor used the local image statistics to achieve soft-adaptation from homogeneous to highly heterogeneous areas. Finally, the results showed that the proposed method, named GNDShrink, yielded a signal-to-noise ratio (SNR) gain of 0.42 dB over the best state-of-the-art despeckling method reported in the literature, 1.73 dB over the Lee filter and 1.31 dB over the Kaun filter at an input SNR of 12.0 dB, when tested on a US image. Further, the visual comparison of despeckled US images indicated that the new method suppressed the speckle noise well, while preserving the texture and organ surfaces.     

Detail-enhanced multimodality medical image fusion based on gradient minimization smoothing filter and shearing filter

In this paper, a detail-enhanced multimodality medical image fusion algorithm is proposed by using proposed multi-scale joint decomposition framework (MJDF) and shearing filter (SF). The MJDF constructed with gradient minimization smoothing filter (GMSF) and Gaussian low-pass filter (GLF) is used to decompose source images into low-pass layers, edge layers, and detail layers at multiple scales. In order to highlight the detail information in the fused image, the edge layer and the detail layer in each scale are weighted combined into a detail-enhanced layer. As directional filter is effective in capturing salient information, so SF is applied to the detail-enhanced layer to extract geometrical features and obtain directional coefficients. Visual saliency map-based fusion rule is designed for fusing low-pass layers, and the sum of standard deviation is used as activity level measurement for directional coefficients fusion. The final fusion result is obtained by synthesizing the fused low-pass layers and directional coefficients. Experimental results show that the proposed method with shift-invariance, directional selectivity, and detail-enhanced property is efficient in preserving and enhancing detail information of multimodality medical images.

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Graphical abstract The detailed implementation of the proposed medical image fusion algorithm.

     

基于小波的医学超声图像斑点噪声抑制方法

斑点噪声是超声图像中固有的噪声。本文提出了一种新的去除斑点噪声的方法，这种方法结合中值滤波和多尺度非线性小波软阈值的优点，首先把原网像进行对数转换，然后把对数转换后的图像进行中值滤波处理，从而把转换后的图像分成两部分，对每一部分进行小波分析，假设小波系数服从广义高斯分布（GGD），利用小波系数的统计特性估计出各个部分各个尺度的阈值，最后用软阈值方法对上述两部分分别去噪。实验结果表明，本文提出的方法在有效去除斑点噪声方面，优于中值滤波，维纳滤波和多尺度非线性阈值算法（MSSNT-A）。     

Performance improvement of the SPIHT coder based on statistics of medical ultrasound images in the wavelet domain

This paper proposes some modifications to the state-of-the-art Set Partitioning In Hierarchical Trees (SPIHT) image coder based on statistical analysis of the wavelet coefficients across various subbands and scales, in a medical ultrasound (US) image. The original SPIHT algorithm codes all the subbands with same precision irrespective of their significance, whereas the modified algorithm processes significant subbands with more precision and ignores the least significant subbands. The statistical analysis shows that most of the image energy in ultrasound images lies in the coefficients of vertical detail subbands while diagonal subbands contribute negligibly towards total image energy. Based on these statistical observations, this work presents a new modified SPIHT algorithm, which codes the vertical subbands with more precision while neglecting the diagonal subbands. This modification speeds up the coding/decoding process as well as improving the quality of the reconstructed medical image at low bit rates. The experimental results show that the proposed method outperforms the original SPIHT on average by 1.4 dB at the matching bit rates when tested on a series of medical ultrasound images. Further, the proposed algorithm needs 33% less memory as compared to the original SPIHT algorithm.     

Performance improvement of the SPIHT coder based on statistics of medical ultrasound images in the wavelet domain

This paper proposes some modifications to the state-of-the-art Set Partitioning In Hierarchical Trees (SPIHT) image coder based on statistical analysis of the wavelet coefficients across various subbands and scales, in a medical ultrasound (US) image. The original SPIHT algorithm codes all the subbands with same precision irrespective of their significance, whereas the modified algorithm processes significant subbands with more precision and ignores the least significant subbands. The statistical analysis shows that most of the image energy in ultrasound images lies in the coefficients of vertical detail subbands while diagonal subbands contribute negligibly towards total image energy. Based on these statistical observations, this work presents a new modified SPIHT algorithm, which codes the vertical subbands with more precision while neglecting the diagonal subbands. This modification speeds up the coding/decoding process as well as improving the quality of the reconstructed medical image at low bit rates. The experimental results show that the proposed method outperforms the original SPIHT on average by 1.4 dB at the matching bit rates when tested on a series of medical ultrasound images. Further, the proposed algorithm needs 33% less memory as compared to the original SPIHT algorithm.     

利用金字塔方法增强DR图像

目的:数字化X线图像(DR)空间分辩率高、动态范围宽,对其进行影像增强处理能提取丰富的临床诊断信息,对疾病诊断,特别是早期病灶的发现提供良好的诊断依据。为此,本文提出了一种基于多尺度方法的DR图像增强算法。方法:构建高斯金字塔和拉普拉斯金字塔,利用特定函数调整拉普拉斯金字塔的系数,根据两个金字塔构成的图像序列,通过反复扩展图像并将结果加起来而重建原始图像,增强图像细节。结论:本文通过多尺度图象增强算法,扩展了DR图像的有用信息,突出了图像细节,为临床诊断提供了实用的增强显示效果。     

Wavelet based compression of medical ultrasound images using vector quantization

In this paper, an efficient technique for compression of medical ultrasound (US) images is proposed. The technique is based on wavelet transform of the original image combined with vector quantization (VQ) of high-energy subbands using the LBG algorithm. First, we analyse the statistical behaviour of wavelet coefficients in US images across various subbands and scales. The analysis show that most of the image energy is concentrated in one of the detail subband, either in the vertical detail subband (most of the time) or in the horizontal subband. The other two subbands at each decomposition level contribute negligibly to the total image energy. Then, by exploiting this statistical analysis, a low-complexity image coder is designed, which applies VQ only to the highest energy subband while discarding the other detail subbands at each level of decomposition. The coder is tested on a series of abdominal and uterus greyscale US images. The experimental results indicate that the proposed method clearly outperforms the JPEG2000 (Joint Photographers Expert Group) encoder both qualitatively and quantitatively. For example, without using any entropy coder, the proposed method yields a peak signal to noise ratio gain of 0.2 dB to 1.2 dB over JPEG2000 on medical US images.     

小波先验在OSL重建算法中的应用

背景：MAP(最大后验)统计重建方法可以在重建过程中引入合适的先验知识达到去除噪声的目的。 目的：根据小波系数的统计特性及能量平衡的原理对高频信息做相应的处理,并将多尺度的小波先验应用到OSL重建算法中以去除噪声。 方法：实验从“变换域”的思想出发,在小波域上根据小波系数的统计特性及能量平衡原理对不同尺度的高频信息做相应的处理,并利用处理后的小波系数进行小波重建。 结果与结论：基于小波先验的OSL算法比ML-EM算法重建的图像与测试模型的误差变小、相关性变大、噪声变少,重建图像变得比较平滑,视觉效果较清楚。     

A singular K-space model for fast reconstruction of magnetic resonance images from undersampled data

Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data.

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Graphical abstract Two Real Images and their sparsified images by singularizing operator

     

A wavelet-based spatially adaptive method for mammographic contrast enhancement

A method aimed at minimizing image noise while optimizing contrast of image features is presented. The method is generic and it is based on local modification of multiscale gradient magnitude values provided by the redundant dyadic wavelet transform. Denoising is accomplished by a spatially adaptive thresholding strategy, taking into account local signal and noise standard deviation. Noise standard deviation is estimated from the background of the mammogram. Contrast enhancement is accomplished by applying a local linear mapping operator on denoised wavelet magnitude values. The operator normalizes local gradient magnitude maxima to the global maximum of the first scale magnitude subimage. Coefficient mapping is controlled by a local gain limit parameter. The processed image is derived by reconstruction from the modified wavelet coefficients. The method is demonstrated with a simulated image with added Gaussian noise, while an initial quantitative performance evaluation using 22 images from the DDSM database was performed. Enhancement was applied globally to each mammogram, using the same local gain limit value. Quantitative contrast and noise metrics were used to evaluate the quality of processed image regions containing verified lesions. Results suggest that the method offers significantly improved performance over conventional and previously reported global wavelet contrast enhancement methods. The average contrast improvement, noise amplification and contrast-to-noise ratio improvement indices were measured as 9.04, 4.86 and 3.04, respectively. In addition, in a pilot preference study, the proposed method demonstrated the highest ranking, among the methods compared. The method was implemented in C++ and integrated into a medical image visualization tool.     

Homomorphic wavelet thresholding technique for denoising medical ultrasound images

A novel homomorphic wavelet thresholding technique for reducing speckle noise in medical ultrasound images is presented. First, we show that the speckle wavelet coefficients in the logarithmically transformed ultrasound images are best described by the Nakagami family of distributions. By exploiting this speckle model and the Laplacian signal prior, a closed form, data-driven, and spatially adaptive threshold is derived in the Bayesian framework. The spatial adaptivity allows the additional information of the image (such as identification of homogeneous or heterogeneous regions) to be incorporated into the algorithm. Further, the threshold has been extended to the redundant wavelet representation, which yields better results than the decimated wavelet transform. Experimental results demonstrate the improved performance of the proposed method over other well-known speckle reduction filters. The application of the proposed method to a realistic US test image shows that the new technique, named HomoGenThresh, outperforms the best wavelet-based denoising method reported in [1] by more than 1.6 dB, Lee filter by 3.6 dB, Kaun filter by 3.1 dB and band-adaptive soft thresholding [2] by 2.1 dB at an input signal-to-noise ratio (SNR) of 13.6 dB.     

Wavelet-based statistical approach for speckle reduction in medical ultrasound images

A novel speckle-reduction method is introduced, based on soft thresholding of the wavelet coefficients of a logarithmically transformed medical ultrasound image. The method is based on the generalised Gaussian distributed (GGD) modelling of sub-band coefficients. The method used was a variant of the recently published BayesShrink method by Chang and Vetterli, derived in the Bayesian framework for denoising natural images. It was scale adaptive, because the parameters required for estimating the threshold depend on scale and sub-band data. The threshold was computed by Kσ/σ_x, where σ and σ_x were the standard deviation of the noise and the sub-band data of the noise-free image, respectively, and K was a scale parameter. Experimental results showed that the proposed method outperformed the median filter and the homomorphic Wiener filter by 29% in terms of the coefficient of correlation and 4% in terms of the edge preservation parameter. The numerical values of these quantitative parameters indicated the good feature preservation performance of the algorithm, as desired for better diagnosis in medical image processing.     

Mammographic Image Denoising and Enhancement Using the Anscombe Transformation, Adaptive Wiener Filtering, and the Modulation Transfer Function

A new restoration methodology is proposed to enhance mammographic images through the improvement of contrast features and the simultaneous suppression of noise. Denoising is performed in the first step using the Anscombe transformation to convert the signal-dependent quantum noise into an approximately signal-independent Gaussian additive noise. In the Anscombe domain, noise is filtered through an adaptive Wiener filter, whose parameters are obtained by considering local image statistics. In the second step, a filter based on the modulation transfer function of the imaging system in the whole radiation field is applied for image enhancement. This methodology can be used as a preprocessing module for computer-aided detection (CAD) systems to improve the performance of breast cancer screening. A preliminary assessment of the restoration algorithm was performed using synthetic images with different levels of quantum noise. Afterward, we evaluated the effect of the preprocessing on the performance of a previously developed CAD system for clustered microcalcification detection in mammographic images. The results from the synthetic images showed an increase of up to 11.5 dB (p = 0.002) in the peak signal-to-noise ratio. Moreover, the mean structural similarity index increased up to 8.3 % (p < 0.001). Regarding CAD performance, the results suggested that the preprocessing increased the detectability of microcalcifications in mammographic images without increasing the false-positive rates. Receiver operating characteristic analysis revealed an average increase of 14.1 % (p = 0.01) in overall CAD performance when restored image sets were used.     

Research of fetal ECG extraction using wavelet analysis and adaptive filtering

Extracting clean fetal electrocardiogram (ECG) signals is very important in fetal monitoring. In this paper, we proposed a new method for fetal ECG extraction based on wavelet analysis, the least mean square (LMS) adaptive filtering algorithm, and the spatially selective noise filtration (SSNF) algorithm. First, abdominal signals and thoracic signals were processed by stationary wavelet transform (SWT), and the wavelet coefficients at each scale were obtained. For each scale, the detail coefficients were processed by the LMS algorithm. The coefficient of the abdominal signal was taken as the original input of the LMS adaptive filtering system, and the coefficient of the thoracic signal as the reference input. Then, correlations of the processed wavelet coefficients were computed. The threshold was set and noise components were removed with the SSNF algorithm. Finally, the processed wavelet coefficients were reconstructed by inverse SWT to obtain fetal ECG. Twenty cases of simulated data and 12 cases of clinical data were used. Experimental results showed that the proposed method outperforms the LMS algorithm: (1) it shows improvement in case of superposition R-peaks of fetal ECG and maternal ECG; (2) noise disturbance is eliminated by incorporating the SSNF algorithm and the extracted waveform is more stable; and (3) the performance is proven quantitatively by SNR calculation. The results indicated that the proposed algorithm can be used for extracting fetal ECG from abdominal signals.     

Application of the EM algorithm to radiographic images.

The expectation maximization (EM) algorithm has received considerable attention in the area of positron emitted tomography (PET) as a restoration and reconstruction technique. In this paper, the restoration capabilities of the EM algorithm when applied to radiographic images is investigated. This application does not involve reconstruction. The performance of the EM algorithm is quantitatively evaluated using a "perceived" signal-to-noise ratio (SNR) as the image quality metric. This perceived SNR is based on statistical decision theory and includes both the observer's visual response function and a noise component internal to the eye-brain system. For a variety of processing parameters, the relative SNR (ratio of the processed SNR to the original SNR) is calculated and used as a metric to compare quantitatively the effects of the EM algorithm with two other image enhancement techniques: global contrast enhancement (windowing) and unsharp mask filtering. The results suggest that the EM algorithm's performance is superior when compared to unsharp mask filtering and global contrast enhancement for radiographic images which contain objects smaller than 4 mm.     

非局部主成分分析极大似然估计MRI图像Rician噪声去噪

由于MRI图像中噪声呈Rician分布,直接使用现有针对高斯噪声的去噪方法将引入误差。基于此本研究使用Rician噪声模型改进现有极大似然估计去噪的高斯模型,同时引入非局部主成分分析,在非局部区域选择灰度和纹理均具有较高相似性的像素进行最优复原估计。使用非局部主成分分析不仅克服现有局部性去噪方法模糊边界的缺陷,而且具有更高的图像细节信息复原能力。分别应用所提出的方法、局部极大似然估计去除Rician噪声方法、采用参数修正非局部均值去除Rician噪声方法、无特定噪声模型的全变差方法,对不同噪声等级和不同纹理复杂度的图像进行定性和定量的去噪实验。结果表明,所提出的方法可在保持图像细节和纹理信息的前提下有效去噪,较之现有方法效果更好。