Speckle reduction of ultrasound images based on Rayleigh-trimmed anisotropic diffusion filter

A novel method is proposed to reduce speckle in ultrasound images. Based on the assumption of Rayleigh distribution of speckle, a Rayleigh-trimmed filter is first proposed to estimate the relative standard deviations of local signals and the results are used to determine the parameter that controls an alpha-trimmed mean filter for suppressing the primary noise. Then the anisotropic diffusion is subsequently applied to further reduce noise while enhancing features and structures in the original image. We also extend the proposed method to three-dimensional space by introducing time as one additional dimension. The proposed method effectively utilizes the statistical characteristics of speckle and the two-step despeckling algorithm reduces speckle significantly while retaining important features. The effectiveness of the proposed method is well demonstrated by experiments on both simulated and real ultrasound images.     

Fractional subpixel diffusion and fuzzy logic approach for ultrasound speckle reduction

Speckle is the dominant source of noise in ultrasound imaging and is a kind of multiplicative noise. It is difficult to design a filter to remove speckle effectively. In this paper, a novel fuzzy subpixel fractional partial difference (FSFPD) for ultrasound speckle reduction is proposed. Euler-Lagrange equation acts as an increasing function of the fractional derivative's absolute value of the image intensity function. The fractional order partial difference is computed in the frequency and fuzzy domain with subpixel precision. We test the proposed method on both synthetic and real breast ultrasound (BUS) images. The comparisons of the experimental results show that the proposed method can preserve edges and structural details of ultrasound images well while removing speckle noise. In addition, the filtered images are assessed and evaluated by radiologists using double blind method. The results demonstrate that the discrimination rate of breast cancers has been highly improved after employing the proposed method.     

Non-local adaptive structure tensors : Application to anisotropic diffusion and shock filtering

Structure tensors are used in several PDE-based methods to estimate information on the local structure in the image, such as edge orientation. They have become a common tool in many image processing applications. To integrate the local data information, the structure tensor is based on a local regularization of a tensorial product. In this paper, we propose a new regularization model based on the non-local properties of the tensor product. The resulting non-local structure tensor is effective in the restitution of the non homogeneity of the local orientation of the structures. It is particularly efficient in texture regions where patches repeat non locally. The new tensor regularization also offers the advantage of automatically adapting the smoothing parameter to the local structures of the tensor product. Finally, we explain how this new adaptive structure tensor can be plugged into two PDEs: an anisotropic diffusion and a shock filter. Comparisons with other tensor regularization methods and other PDEs demonstrate the clear advantage of using the non-local structure tensor.     

A diffusion stick method for speckle suppression in ultrasonic images

This paper presents a diffusion stick method for speckle suppression in ultrasonic images. An asymmetric stick filter kernel is firstly defined by decomposing the rectangle neighborhood into line segments of variable orientations. Then, the weighted sum of averages along each stick is used to produce the filtered images. Implemented in an iteration scheme, our method works as a pseudo-diffusion process, where the diffusivity is controlled by a normalized variance function. Experiments of synthetic and real images show that the diffusion stick technique performs effectively in suppressing speckle noise, preserving resolvable structures and enhancing linear features.     

A semi-discrete tailored finite point method for a class of anisotropic diffusion problems

This work proposes a tailored finite point method (TFPM) for the numerical solution of an anisotropic diffusion problem, which has much smaller diffusion coefficient along one direction than the other on a rectangular domain. The paper includes analysis on the differentiability of the solution to the given problem under some compatibility conditions. It has detailed derivation for a semi-discrete TFPM for the given problem. This work also proves a uniform error estimate on the approximate solution. Numerical results show that the TFPM is accurate as well as efficient for the strongly anisotropic diffusion problem. Examples include those that do not satisfy compatibility and regularity conditions. For the incompatible problems, numerical experiments indicate that the method proposed can still offer good numerical approximations.     

Surface motion of single crystals driven by anisotropic surface diffusion

In this paper we compute a mathematical model for the evolution of single crystal with a particular kind of anisotropic surface free energies that yields equilibrium crystal shapes close to octahedrons. Employing the developed model we exhibit the entire evolution path of single crystals to equilibrium with different levels of anisotropic surface free energy. We find that with a mildly anisotropic surface free energy, the crystal morphology is smooth in evolution and evolves to a unique equilibrium crystal shape. With a severely anisotropic surface free energy, edges, corners and faceting by hill-and-valley structures on crystal surface occur. The equilibrium crystal shape reached in computation approaches the analytic octahedron Wulff shape as the anisotropy in the surface free energy becomes more severe.      

Parallel simulation of anisotropic diffusion with human brain DT-MRI Data

We conduct simulations for the 3D unsteady state anisotropic diffusion process with DT-MRI data in the human brain by discretizing the governing diffusion equation on Cartesian grid and adopting a high performance differential-algebraic equation (DAE) solver, the parallel version of implicit differential-algebraic (IDA) solver, to tackle the resulting large scale system of DAEs. Parallel preconditioning techniques including sparse approximate inverse and banded-block-diagonal preconditioners are used with the GMRES method to accelerate the convergence rate of the iterative solution. We then investigate and compare the efficiency and effectiveness of the two parallel preconditioners. The experimental results of the diffusion simulations on a parallel supercomputer show that the sparse approximate inverse preconditioning strategy, which is robust and efficient with good scalability, gives a much better overall performance than the banded-block-diagonal preconditioner.     

Finding out general tendencies in speckle noise reduction in ultrasound images

This article investigates and compiles some of the techniques mostly used in the smoothing or suppression of speckle noise in ultrasound images. With this information, a comparison of all the methods studied is done based on an experiment, using quality metrics to test their performance and show the benefits each one can contribute. To test the methods, a synthetic, noise-free image of a kidney is created and later simulations using Field II program to corrupt it are performed. This way, the smoothing techniques can be compared using numeric metrics, taking the noise-free image as a reference. Since real ultrasound images are already noise corrupted images and real noise-free images do not exist, conventional metrics cannot be used to indicate the quality obtained with filtering. Nevertheless, we propose the use of the tendencies observed in our study in real images.     

Micro-crack inspection in heterogeneously textured solar wafers using anisotropic diffusion

This paper proposes a machine vision scheme for detecting micro-crack defects in solar wafer manufacturing. The surface of a polycrystalline silicon wafer shows heterogeneous textures, and the shape of a micro-crack is similar to the multi-grain background. They make the automated visual inspection task extremely difficult.     

Scale selection for anisotropic diffusion filter by Markov random field model

The selection of stopping time (i.e., scale) significantly affects the performance of anisotropic diffusion filter for image denoising. This paper designs a Markov random field (MRF) scale selection model, which selects scales for image segments, then the denoised image is the composition of segments at their optimal scales in the scale space. Firstly, statistics-based scale selection criteria are proposed for image segments. Then we design a scale selection energy function in the MRF framework by considering the scale coherence between neighboring segments. A segment-based noise estimation algorithm is also developed to estimate the noise statistics efficiently. Experiments show that the performance of MRF scale selection model is much better than the previous global scale selection schemes. Combined with this scale selection model, the anisotropic diffusion filter is comparable to or even outperform the state-of-the-art denoising methods in performance.     

基于改进各向异性扩散的超声医学图像滤波方法

为了能有效地去除超声医学图像中的噪声,又能较好地保持图像的边缘和重要细节信息,在η-ξ正交坐标系下研究并分析了各向异性扩散模型(P-M模型)的扩散滤波机制,并在此坐标系下建立了一种新的各向异性扩散滤波方案。实验结果表明,改进的扩散模型不仅能够有效地保持图像边缘,而且还能够克服P-M模型对小尺寸噪声的敏感问题。     

A novel method for speckle noise reduction and ship target detection in SAR images

It is very difficult to detect small targets when the scattering intensity of background clutter is as strong as the targets and the speckle noise is serious in synthetic aperture radar (SAR) images. Because the scattering of man-made objects lasts for a longer time than that of background clutter in azimuth matching scope, it is much easier for man-made objects to produce strong coherence than ground objects. As the essence of SAR imaging is coherent imaging, the contrast between targets and background clutter can be enhanced via coherent processing of SAR images. This paper proposes a novel method to reduce speckle noise for SAR images and to improve the detected ratio for SAR ship targets from the SAR imaging mechanism. This new method includes the coherence reduction speckle noise (CRSN) algorithm and the coherence constant false-alarm ratio (CCFAR) detection algorithm. Real SAR image data is used to test the presented algorithms and the experimental results verify that they are feasible and effective.     

Robust anisotropic diffusion to produce enhanced statistical parametric map from noisy fMRI

This paper presents a new, simple, and elegant technique to obtain enhanced statistical parametric maps (SPMs) from noisy functional magnetic resonance imaging (fMRI) data. This technique is based on the robust anisotropic diffusion (RAD), a technique normally used as an edge-preserving filter. A direct application of the RAD to the fMRI data does not work, because in this case RAD would perform an edge-preserving filtering of the fMRI structural information, instead of enhancing its functional information. The RAD can be applied directly to SPM but, in this case, only a small improvement of the SPM quality can be achieved, because the originating fMRI is not taken into account. To overcome these difficulties, we propose to estimate the SPM from the noisy fMRI, compute the diffusion coefficients in the SPM space, and then perform the diffusion in the structural information-removed fMRI data using the coefficients previously computed. These steps are iterated until convergence. We have tested the new technique in both simulated and real fMRI images, yielding surprisingly sharp and noiseless SPMs with increased statistical significance. We also describe how to automatically estimate an appropriate scale parameter.     

Seismic noise attenuation by means of an anisotropic non-linear diffusion filter

Noise attenuation is a major seismic data processing concern. In seismic data, noise can appear as random, coherent and/or impulsive. Recently, many different techniques, ranging from relatively simple processes to extremely complex ones, have been used for noise attenuation. Image filtering techniques are relatively new methods in seismic exploration. We introduced the anisotropic non-linear diffusion filter which is an effective way to de-noise images. Since a seismic section can be considered as an image of a two-variable function, we implemented the anisotropic non-linear diffusion filter to reduce both random and Gaussian noises. This filter is shown to be effective in removing noise while preserving edges and hence reducing resolution loss in seismic data. The anisotropic non-linear diffusion filter, with Tukey's function to guide the diffusivity, was applied to synthetic and real seismic data. The results show a signal-to-noise ratio increase with reflector continuity in addition to better recovery of reflector amplitudes even when dealing with complex subsurface geological structures.     

On the robustness of a multigrid method for anisotropic reaction-diffusion problems

In this paper, we consider a reaction-diffusion boundary value problem in a three-dimensional thin domain. The very different length scales in the geometry result in an anisotropy effect. Our study is motivated by a parabolic heat conduction problem in a thin foil leading to such anisotropic reaction-diffusion problems in each time step of an implicit time integration method [7]. The reaction-diffusion problem contains two important parameters, namely ε >0 which parameterizes the thickness of the domain and μ >0 denoting the measure for the size of the reaction term relative to that of the diffusion term. In this paper we analyze the convergence of a multigrid method with a robust (line) smoother. Both, for the W- and the V-cycle method we derive contraction number bounds smaller than one uniform with respect to the mesh size and the parameters ε and μ.      

基于Canny算子的边缘切线扩散医学超声图像去噪

医学超声图像的细节特征在临床诊断中具有重要的意义.针对于传统的PM算法以及各种改进型各向异性去噪方法(Catte_PM、SRAD、CENCD等)存在边缘中的噪声点未作处理,多次迭代产生虚假边缘等缺点,通过分析具有代表性的Catte_PM各向异性模型,提出了一种结合自适应Canny算子,沿图像边缘切线方向扩散的去噪方法.该算法首先通过改进的Canny算子将图像范围分为边缘区和非边缘区;其次改进现有的扩散方法,使扩散方向只沿图像边缘切线方向进行;最后对非边缘区域采用有限次(三次)的各向同性滤波.实验结果表明,该方法能够有效地解决滤波和图像细节保护这一矛盾问题,使得图像质量有较明显的改善.     

基于各向异性改进的水平集超声图像去噪算法

针对各向异性扩散可能出现的阶梯效应以及扩散门限难以准确确定、水平集函数只能根据图像梯度区分图像边缘及同质区域的问题,将各向异性扩散中的边缘增强项引入到水平集方程中,同时自适应地估计扩散门限,在去除噪声的同时保持和增强边缘。该方法结合了水平集函数和各向异性扩散的优点,理论分析和实验结果均表明了该算法的去噪效果更好。     

A priori anisotropic mesh adaptation driven by a higher dimensional embedding

We generalize the higher embedding approach proposed in Lévy and Bonneel (2013) to generate an adapted mesh matching the intrinsic directionalities of an assigned function. In more detail, the original embedding map between the physical (lower dimensional) and the embedded (higher dimensional) setting is modified to include information associated with the function and with its gradient. Then, we set an adaptive procedure, driven by the embedded metric but performed in the lower dimensional setting, which results into an anisotropic adapted mesh of the physical domain. The effectiveness of the proposed procedure is extensively investigated on several two-dimensional test cases, involving both analytical functions and finite element approximations of differential problems. The preliminary verification in three dimensions corroborates the robustness of the method.     

Numerical use of {m,n}-approximation method thermoelastic anisotropic thin shell theory equations represented in a special form

A linear uncoupled quasi-static theory of thermoelastic anisotropic thin shells of constant thickness is formulated. In the derivation of equations and boundary conditions, a variant of the {$m,n$}-approximation method, which is based on the variational principle of the thermoelasticity theory, is used. According to this method, the unknown functions are represented in the form of a series of Legendre polynomials in the transverse coordinate that agree with the force boundary conditions on the facial surfaces. From the system of equations of the constructed theory for generalised displacements, strains, and stresses, a system of equations for generalised displacements is obtained; this system is solved for the second derivatives of generalised displacements with respect to one of the Gaussian parameters of the middle surface. For a system of partial differential equations represented in such a form, the known techniques for the reduction of systems of two-dimensional equations to normal systems of ordinary differential equations, which can be solved by standard numerical methods, can be applied. The system of equations for generalised displacements is reduced to a normal system of ordinary differential equations in the case of a plane deformation of a cylindrical panel. Through the use of these equations and the S. K. Godunov method of orthogonal successive substitutions, the bending problems of a planar beam subjected to a mechanical load or a thermal load and a circular cylindrical panel exposed to a thermal load are numerically solved. It is demonstrated that the proposed equations are particularly suitable for the analysis of boundary effects in planar beams and circular cylindrical panels.