Locally adaptive wavelet domain Bayesian processor for denoising medical ultrasound images using Speckle modelling based on Rayleigh distribution

The authors present a statistical approach to speckle reduction in medical ultrasound B-scan images based on maximum a posteriori (MAP) estimation in the wavelet domain. In this framework, a new class of statistical model for speckle noise is proposed to obtain a simple and tractable solution in a closed analytical form. The proposed method uses the Rayleigh distribution for speckle noise and a Gaussian distribution for modelling the statistics of wavelet coefficients in a logarithmically transformed ultrasound image. The method combines the MAP estimation with the assumption that speckle is spatially correlated within a small window and designs a locally adaptive Bayesian processor whose parameters are computed from the neighboring coefficients. Further, the locally adaptive estimator is extended to the redundant wavelet representation, which yields better results than the decimated wavelet transform. The experimental results show that the proposed method clearly outperforms the state-of-the-art medical image denoising algorithm of Pizurica et al., spatially adaptive single-resolution methods and band-adaptive multi-scale soft-thresholding techniques in terms of quantitative performance as well as in terms of visual quality of the images. The main advantage of the new method over the existing techniques is that it suppresses speckle noise well, while retaining the structure of the image, particularly the thin bright streaks, which tend to occur along boundaries between tissue layers.     

Despeckling of medical ultrasound images using Daubechies complex wavelet transform

The paper presents a novel despeckling method, based on Daubechies complex wavelet transform, for medical ultrasound images. Daubechies complex wavelet transform is used due to its approximate shift invariance property and extra information in imaginary plane of complex wavelet domain when compared to real wavelet domain. A wavelet shrinkage factor has been derived to estimate the noise-free wavelet coefficients. The proposed method firstly detects strong edges using imaginary component of complex scaling coefficients and then applies shrinkage on magnitude of complex wavelet coefficients in the wavelet domain at non-edge points. The proposed shrinkage depends on the statistical parameters of complex wavelet coefficients of noisy image which makes it adaptive in nature. Effectiveness of the proposed method is compared on the basis of signal to mean square error (SMSE) and signal to noise ratio (SNR). The experimental results demonstrate that the proposed method outperforms other conventional despeckling methods as well as wavelet based log transformed and non-log transformed methods on test images. Application of the proposed method on real diagnostic ultrasound images has shown a clear improvement over other methods.     

Chromosome image enhancement using multiscale differential operators

Chromosome banding patterns are very important features for karyotyping, based on which cytogenetic diagnosis procedures are conducted. Due to cell culture, staining, and imaging conditions, image enhancement is a desirable preprocessing step before performing chromosome classification. In this paper, we apply a family of differential wavelet transforms (Wang and Lee, 1998), (Wang, 1999) for this purpose. The proposed differential filters facilitate the extraction of multiscale geometric features of chromosome images. Moreover, desirable fast computation can be realized. We study the behavior of both banding edge pattern and noise in the wavelet transform domain. Based on the fact that image geometrical features like edges are correlated across different scales in the wavelet representation, a multiscale point-wise product (MPP) is used to characterize the correlation of the image features in the scale-space. A novel algorithm is proposed for the enhancement of banding patterns in a chromosome image. In order to compare objectively the performance of the proposed algorithm against several existing image-enhancement techniques, a quantitative criteria, the contrast improvement ratio (CIR), has been adopted to evaluate the enhancement results. The experimental results indicate that the proposed method consistently outperforms existing techniques in terms of the CIR measure, as well as in visual effect. The effect of enhancement on cytogenetic diagnosis is further investigated by classification tests conducted prior to and following the chromosome image enhancement. In comparison with conventional techniques, the proposed method leads to better classification results, thereby benefiting the subsequent cytogenetic diagnosis.     

Multi-spectral and hyperspectral image fusion using 3-D wavelet transform

Image fusion is performed between one band of multi-spectral image and two bands of hyperspectral image to produce fused image with the same spatial resolution as source multi-spectral image and the same spectral resolution as source hyperspeetral image. According to the characteristics and 3-Dimensional （3-D） feature analysis of multi-spectral and hyperspectral image data volume, the new fusion approach using 3-D wavelet based method is proposed. This approach is composed of four major procedures： Spatial and spectral resampling, 3-D wavelet transform, wavelet coefficient integration and 3-D inverse wavelet transform. Especially, a novel method, Ratio Image Based Spectral Resampling （RIBSR）method, is proposed to accomplish data resampling in spectral domain by utilizing the property of ratio image. And a new fusion rule, Average and Substitution （A＆S） rule, is employed as the fusion rule to accomplish wavelet coefficient integration. Experimental results illustrate that the fusion approach using 3-D wavelet transform can utilize both spatial and spectral characteristics of source images more adequately and produce fused image with higher quality and fewer artifacts than fusion approach using 2-D wavelet transform. It is also revealed that RIBSR method is capable of interpolating the missing data more effectively and correctly, and A＆S rule can integrate coefficients of source images in 3-D wavelet domain to preserve both spatial and spectral features of source images more properly.     

基于改进小波变换的医学图像融合算法研究

本文主要针对图像经过小波变换后边角上看不清楚和传统的边缘检测算法对噪声敏感的问题,结合医学图像的特点,提出一种小波变换的修正算法。首先采用改进的多结构元多尺度形态学梯度的边缘检测进行图像的预处理,其次对CT图像和MRI图像分别进行两种不同小波基的三层小波分解;接着求其对应分量系数的差值图像,最后按着一定加权融合系数对差值图像进行融合得到最终的融合图像。实验结果和评价参数表明,这种改进的医学图像融合算法相比于传统的多小波融合算法不仅强化了融合图像的边缘和纹理特征,提高了分辨率,而且有效地保留了原图像的信息。     

Image Restoration by Lifting‐Based Wavelet Domain E‐Median Filter

In this paper, we propose a method of applying a lifting‐based wavelet domain e‐median filter (LBWDEMF) for image restoration. LBWDEMF helps in reducing the number of computations. An e‐median filter is a type of modified median filter that processes each pixel of the output of a standard median filter in a binary manner, keeping the output of the median filter unchanged or replacing it with the original pixel value. Binary decision‐making is controlled by comparing the absolute difference of the median filter output and the original image to a preset threshold. In addition, the advantage of LBWDEMF is that probabilities of encountering root images are spread over sub‐band images, and therefore the e‐median filter is unlikely to encounter root images at an early stage of iterations and generates a better result as iteration increases. The proposed method transforms an image into the wavelet domain using lifting‐based wavelet filters, then applies an e‐median filter in the wavelet domain, transforms the result into the spatial domain, and finally goes through one spatial domain e‐median filter to produce the final restored image. Moreover, in order to validate the effectiveness of the proposed method we compare the result obtained using the proposed method to those using a spatial domain median filter (SDMF), spatial domain e‐median filter (SDEMF), and wavelet thresholding method. Experimental results show that the proposed method is superior to SDMF, SDEMF, and wavelet thresholding in terms of image restoration.     

基于深度多级小波变换的图像盲去模糊算法

近年来卷积神经网络广泛应用于单幅图像去模糊问题,卷积神经网络的感受野大小、网络深度等会影响图像去模糊算法性能。为了增大感受野以提高图像去模糊算法的性能,该文提出一种基于深度多级小波变换的图像盲去模糊算法。将小波变换嵌入编-解码结构中,在增大感受野的同时加强图像特征的稀疏性。为在小波域重构高质量图像,该文利用多尺度扩张稠密块提取图像的多尺度信息,同时引入特征融合块以自适应地融合编-解码之间的特征。此外,由于小波域和空间域对图像信息的表示存在差异,为融合这些不同的特征表示,该文利用空间域重建模块在空间域进一步提高重构图像的质量。实验结果表明该文方法在结构相似度(SSIM)和峰值信噪比(PSNR)上具有更好的性能,而且在真实模糊图像上具有更好的视觉效果。

     

一种小波域与空域相结合的图像滤波方法

利用小波阈值去噪方法和传统空间域Lee 滤波的特点, 提出了一种图像去噪的的组合滤波方案。首先在小波域对图像阈值去噪, 得到预去噪图像; 再在空间域上利用自适应Wiener 滤波器进一步提高恢复图像的精度。为了保证小波域和空间域两种算法之间的匹配, 对预去噪图像中残留噪声的分布进行了研究, 对其噪声方差估计做了改进, 提出了一种估计噪声方差的近似最优公式。仿真实验表明, 与单独的在小波域或空域去噪相比, 该方法的均方误差和信噪比指标均得到了改善。     

Modeling and reduction of SAR interferometric phase noise in the wavelet domain

This paper addresses the problem of interferometric phase noise reduction in synthetic aperture radar interferometry. A new phase noise model in the complex domain is introduced and validated by using both simulated and real interferograms. This noise model is also derived in the complex wavelet domain, where a novel noise reduction algorithm, which is not based on a windowing process and without the necessity of phase unwrapping, is addressed. The use of the wavelet transform allows to maintain the spatial resolution in the filtered phase image and prevents to filter low coherence areas. By using both, simulated as well as real interferometric phase images, the performance of this algorithm, in terms of noise reduction, spatial resolution maintenance, and computational efficiency, is reported and compared with other conventional filtering approaches.     

一种小波域与空域相结合的图像滤波方法

利用小波阈值去噪方法和传统空间域Lee滤波的特点,提出了一种图像去噪的的组合滤波方案。首先在小波域对图像阈值去噪,得到预去噪图像;再在空间域上利用自适应Wiener滤波器进一步提高恢复图像的精度。为了保证小波域和空间域两种算法之间的匹配,对预去噪图像中残留噪声的分布进行了研究,对其噪声方差估计做了改进,提出了一种估计噪声方差的近似最优公式。仿真实验表明,与单独的在小波域或空域去噪相比,该方法的均方误差和信噪比指标均得到了改善。     

Combining spatial and scale-space techniques for edge detection to provide a spatially adaptive wavelet-based noise filtering algorithm

New methods for detecting edges in an image using spatial and scale-space domains are proposed. A priori knowledge about geometrical characteristics of edges is used to assign a probability factor to the chance of any pixel being on an edge. An improved double thresholding technique is introduced for spatial domain filtering. Probabilities that pixels belong to a given edge are assigned based on pixel similarity across gradient amplitudes, gradient phases and edge connectivity. The scale-space approach uses dynamic range compression to allow wavelet correlation over a wider range of scales. A probabilistic formulation is used to combine the results obtained from filtering in each domain to provide a final edge probability image which has the advantages of both spatial and scale-space domain methods. Decomposing this edge probability image with the same wavelet as the original image permits the generation of adaptive filters that can recognize the characteristics of the edges in all wavelet detail and approximation images regardless of scale. These matched filters permit significant reduction in image noise without contributing to edge distortion. The spatially adaptive wavelet noise-filtering algorithm is qualitatively and quantitatively compared to a frequency domain and two wavelet based noise suppression algorithms using both natural and computer generated noisy images.     

Feature-based wavelet shrinkage algorithm for image denoising.

A selective wavelet shrinkage algorithm for digital image denoising is presented. The performance of this method is an improvement upon other methods proposed in the literature and is algorithmically simple for large computational savings. The improved performance and computational speed of the proposed wavelet shrinkage algorithm is presented and experimentally compared with established methods. The denoising method incorporated in the proposed algorithm involves a two-threshold validation process for real-time selection of wavelet coefficients. The two-threshold criteria selects wavelet coefficients based on their absolute value, spatial regularity, and regularity across multiresolution scales. The proposed algorithm takes image features into consideration in the selection process. Statistically, most images have regular features resulting in connected subband coefficients. Therefore, the resulting subbands of wavelet transformed images in large part do not contain isolated coefficients. In the proposed algorithm, coefficients are selected due to their magnitude, and only a subset of those selected coefficients which exhibit a spatially regular behavior remain for image reconstruction. Therefore, two thresholds are used in the coefficient selection process. The first threshold is used to distinguish coefficients of large magnitude and the second is used to distinguish coefficients of spatial regularity. The performance of the proposed wavelet denoising technique is an improvement upon several other established wavelet denoising techniques, as well as being computationally efficient to facilitate real-time image-processing applications.     

Despeckling of medical ultrasound images using data and rate adaptive lossy compression

A novel technique for despeckling the medical ultrasound images using lossy compression is presented. The logarithm of the input image is first transformed to the multiscale wavelet domain. It is then shown that the subband coefficients of the log-transformed ultrasound image can be successfully modeled using the generalized Laplacian distribution. Based on this modeling, a simple adaptation of the zero-zone and reconstruction levels of the uniform threshold quantizer is proposed in order to achieve simultaneous despeckling and quantization. This adaptation is based on: (1) an estimate of the corrupting speckle noise level in the image; (2) the estimated statistics of the noise-free subband coefficients; and (3) the required compression rate. The Laplacian distribution is considered as a special case of the generalized Laplacian distribution and its efficacy is demonstrated for the problem under consideration. Context-based classification is also applied to the noisy coefficients to enhance the performance of the subband coder. Simulation results using a contrast detail phantom image and several real ultrasound images are presented. To validate the performance of the proposed scheme, comparison with two two-stage schemes, wherein the speckled image is first filtered and then compressed using the state-of-the-art JPEG2000 encoder, is presented. Experimental results show that the proposed scheme works better, both in terms of the signal to noise ratio and the visual quality.     

小波域结构相似度融合图像质量评价方法

针对融合图像质量评价问题,分析了图像质量评价与融合图像质量评价的关系,给出了融合图像质量评价方法的一般表达公式,指出构造实际并不存在的参考图像是解决融合图像质量评价问题的关键。在此基础上,基于空域结构相似度评价方法,对输入源图像和融合图像分别进行小波分解,利用输入源图像小波分解系数构造参考图像小波系数,然后根据人眼视觉敏感度带通特性对参考图像和融合图像的各小波频带进行加权,从而得到整幅图像的小波域结构相似度评价指标,利用目标可探测性、细节可分辨能力和图像整体舒适性构成主观评价指标分别和交互信息量、基于空域的结构相似度比较。实验结果表明,相比于传统的客观评价方法,提出的方法所得结果与主观评价结果的一致性更好。     

Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising.

We develop three novel wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. The core of our approach is the estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest." In this respect, we analyze cases where the probability of signal presence is 1) fixed per subband, 2) conditioned on a local spatial context, and 3) conditioned on information from multiple image bands. All the probabilities are estimated assuming a generalized Laplacian prior for noise-free subband data and additive white Gaussian noise. The results demonstrate that the new subband-adaptive shrinkage function outperforms Bayesian thresholding approaches in terms of mean-squared error. The spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity. The performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding.     

利用边缘信息的多尺度分块压缩感知自适应采样方法

在小波域多尺度压缩感知框架下,被完整保留的低频系数存在着许多可利用的图像信息。本文在分析了不同尺度之间、以及同一尺度之内的系数块存在能量差异的基础上,提出了利用边缘信息的多尺度分块压缩感知自适应采样方法(EAS)。该方法首先利用低频系数提取出边缘信息,然后将边缘信息分块,加权计算每个块的边缘信息度,根据边缘信息度判断每个系数块的能量大小,将其转换成每个子块的自适应采样率,从而实现多尺度分块压缩感知的自适应采样。采用医学图像,含有复杂纹理的自然图像和含有严重噪声的SAR图像三类测试数据,验证了EAS方法的性能。数值实验结果表明,EAS方法对不同的压缩感知算法均有很大的提升,能够显著提高图像的重构质量和视觉效果。      

基于单小波和多小波的红外图像盲去噪

Deviation is essential to classic soft threshold denoising in wavelet domain. Texture features of noised image denoised by wavelet transform were weakened. Gibbs effect is distinct at edges of image.Image blurs comparing with original noised image. To solve the questions, a blind denoising method based on single-wavelet transform and multiwavelets transform was proposed. The method doesn't depend on size of image and deviation to determine threshold of wavelet coefficients, which is different from classical soft-threshold denoising in wavelet domain. Moreover, the method is good for many types of noise. Gibbs effect disappeared with this method, edges of image are preserved well, and noise is smoothed and restrained effectively.     

Medical image enhancement algorithm based on wavelet transform

Low contrast and poor quality are main problems in the production of medical images. By using the wavelet transform and Haar transform, a novel image enhancement approach is proposed. First, a medical image was decomposed with wavelet transform. Secondly, all high-frequency sub-images were decomposed with Haar transform. Thirdly, noise in the frequency field was reduced by the soft-threshold method. Fourthly, high-frequency coefficients were enhanced by different weight values in different sub-images. Then, the enhanced image was obtained through the inverse wavelet transform and inverse Haar transform. Lastly, the image's histogram was stretched by nonlinear histogram equalisation. Experiments showed that this method can not only enhance an image?s details but can also preserve its edge features effectively.     

Image denoising with anisotropic bivariate shrinkage

This paper presents a novel image denoising algorithm based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The anisotropic bivariate Laplacian model not only captures the child-parent dependency between wavelet coefficients, but also fits the anisotropic property of the variances of wavelet coefficients in different scales of natural images. With this statistical model, we derive a closed-form anisotropic bivariate shrinkage function in the framework of Bayesian denoising and a new image denoising approach with local marginal variance estimation based on this newly derived shrinkage function is proposed in the discrete wavelet transform (DWT) domain. The proposed anisotropic bivariate shrinkage approach is also extended to the dual-tree complex wavelet transform (DT-CWT) domain to further improve the performance of image denoising. To take full advantage of DT-CWT, a more accurate noise variance estimator is proposed and the way the anisotropic bivariate shrinkage function applied to the magnitudes of DT-CWT coefficients is presented. Experiments were carried out in both the DWT and the DT-CWT domain to validate the effectiveness of the proposed method. Using a representative set of standard test images corrupted by additive white Gaussian noise, the simulation results show that the proposed method provides promising results and is competitive with the best wavelet-based denoising results reported in the literature both in terms of peak signal-to-noise ratio (PSNR) and in visual quality.