Rayleigh-maximum-likelihood filtering for speckle reduction of ultrasound images

Speckle is a multiplicative noise that degrades ultrasound images. Recent advancements in ultrasound instrumentation and portable ultrasound devices necessitate the need for more robust despeckling techniques, for both routine clinical practice and teleconsultation. Methods previously proposed for speckle reduction suffer from two major limitations: 1) noise attenuation is not sufficient, especially in the smooth and background areas; 2) existing methods do not sufficiently preserve or enhance edges--they only inhibit smoothing near edges. In this paper, we propose a novel technique that is capable of reducing the speckle more effectively than previous methods and jointly enhancing the edge information, rather than just inhibiting smoothing. The proposed method utilizes the Rayleigh distribution to model the speckle and adopts the robust maximum-likelihood estimation approach. The resulting estimator is statistically analyzed through first and second moment derivations. A tuning parameter that naturally evolves in the estimation equation is analyzed, and an adaptive method utilizing the instantaneous coefficient of variation is proposed to adjust this parameter. To further tailor performance, a weighted version of the proposed estimator is introduced to exploit varying statistics of input samples. Finally, the proposed method is evaluated and compared to well-accepted methods through simulations utilizing synthetic and real ultrasound data.     

Hybrid Polynomial Filters for Gaussian and Non-Gaussian Noise Environments

Traditional polynomial filtering theory, based on linear combinations of polynomial terms, is able to approximate important classes of nonlinear systems. The linear combination of polynomial terms, however, yields poor performance in environments characterized by Gaussian and heavy tailed distributions. Weighted median and weighted myriad filters, in contrast, are well known for their outlier suppression and detail preservation properties. It is shown here that the weighted median and weighted myriad methodologies are naturally extended to the polynomial sample case, yielding hybrid filter structures that exploits the higher-order statistics of the observed samples while simultaneously being robust to outliers for both Gaussian and heavy-tailed distributions environments. Moreover, the introduced hybrid polynomial filter classes are well motivated by analysis of cross and square term statistics of Gaussian and heavy-tailed distributions. A presented asymptotic tail mass analysis shows that polynomial terms, both under Gaussian and heavy-tailed noise statistics, have heavier tails than the observed samples, indicating that robust combination methods should be utilized to avoid undue influence of outliers. Further analysis shows weighted median processing of polynomial terms for the Gaussian noise case, and weighted median and weighted myriad processing of cross and square terms, respectively, for the heavy-tailed noise case, are justified from a maximum likelihood perspective. Filters parameter optimization procedures are also presented. Finally, the effectiveness of hybrid filters is demonstrated through simulations that include temporal, spectrum, and bispectrum analysis     

Meridian Filtering for Robust Signal Processing

A broad range of statistical processes is characterized by the generalized Gaussian statistics. For instance, the Gaussian and Laplacian probability density functions are special cases of generalized Gaussian statistics. Moreover, the linear and median filtering structures are statistically related to the maximum likelihood estimates of location under Gaussian and Laplacian statistics, respectively. In this paper, we investigate the well-established statistical relationship between Gaussian and Cauchy distributions, showing that the random variable formed as the ratio of two independent Gaussian distributed random variables is Cauchy distributed. We also note that the Cauchy distribution is a member of the generalized Cauchy distribution family. Recently proposed myriad filtering is based on the maximum likelihood estimate of location under Cauchy statistics. An analogous relationship is formed here for the Laplacian statistics, as the ratio of Laplacian statistics yields the distribution referred here to as the Meridian. Interestingly, the Meridian distribution is also a member of the generalized Cauchy family. The maximum likelihood estimate under the obtained statistics is analyzed. Motivated by the maximum likelihood estimate under meridian statistics, meridian filtering is proposed. The analysis presented here indicates that the proposed filtering structure exhibits characteristics more robust than that of median and myriad filtering structures. The statistical and deterministic properties essential to signal processing applications of the meridian filter are given. The meridian filtering structure is extended to admit real-valued weights utilizing the sign coupling approach. Finally, simulations are performed to evaluate and compare the proposed meridian filtering structure performance to those of linear, median, and myriad filtering.     

Polynomial weighted median filtering

This paper extends weighted median (WM) filters to the class of polynomial weighted median (PWM) filters. Traditional polynomial filtering theory, based on linear combinations of polynomial terms, is able to approximate important classes of nonlinear systems. The linear combination of polynomial terms, however, yields poor performance in environments characterized by heavy tailed distributions. Weighted median filters, in contrast, are well known for their outlier suppression and detail preservation properties. The weighted median sample selection methodology is naturally extended to the polynomial sample case, yielding a filter structure that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers. Moreover, the PWM filter class is well motivated by an analysis of cross and square term statistics. A presented probability density function analysis shows that these terms have heavier tails than the observed samples, indicating that robust combination methods should be utilized to avoid undue influence of outliers. Further analysis shows weighted median processing of polynomial terms is justified from a maximum likelihood perspective. The established PWM filter class is statistically analyzed through the determination of the filter output distribution and breakdown probability. Filter parameter optimization procedures are also presented. Finally, the effectiveness of PWM filters is demonstrated through simulations that include temporal, spectrum, and bispectrum analysis.     

Quadratic weighted median filters for edge enhancement of noisy images.

Quadratic Volterra filters are effective in image sharpening applications. The linear combination of polynomial terms, however, yields poor performance in noisy environments. Weighted median (WM) filters, in contrast, are well known for their outlier suppression and detail preservation properties. The WM sample selection methodology is naturally extended to the quadratic sample case, yielding a filter structure referred to as quadratic weighted median (QWM) that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers arising in the higher order statistics of environment noise. Through statistical analysis of higher order samples, it is shown that, although the parent Gaussian distribution is light tailed, the higher order terms exhibit heavy-tailed distributions. The optimal combination of terms contributing to a quadratic system, i.e., cross and square, is approached from a maximum likelihood perspective which yields the WM processing of these terms. The proposed QWM filter structure is analyzed through determination of the output variance and breakdown probability. The studies show that the QWM exhibits lower variance and breakdown probability indicating the robustness of the proposed structure. The performance of the QWM filter is tested on constant regions, edges and real images, and compared to its weighted-sum dual, the quadratic Volterra filter. The simulation results show that the proposed method simultaneously suppresses the noise and enhances image details. Compared with the quadratic Volterra sharpener, the QWM filter exhibits superior qualitative and quantitative performance in noisy image sharpening.     

Experimental calibration and field investigation of the oxygen isotopic fractionation between biogenic aragonite and water

Marine molluscs have long been recognised as potential records of palaeoclimate change using the patterns and differences in the stable isotopic composition of the carbonate shells. The aim of this study is to improve the robustness of this approach for aragonitic molluscs by completing the first experimental calibration of the fractionation between water and biogenic aragonite. Fractionation factors were calibrated by growing specimens of the freshwater mollusc Lymnaea peregra under controlled conditions of water temperature and isotopic composition. Fifteen populations of L. peregra were maintained at constant temperature and isotopic conditions for five months (at five different temperatures and using three different water compositions). Water samples and temperature measurements were taken regularly throughout the experiment. The temperature dependence of the fractionation factor, between 8 and 24 degrees C, is given by: 1000 ln alpha=16.74x(1000T(-1))-26.39 (T in Kelvin) and the relationship between temperature (T), delta(18)O(carb) and delta(18)O(wat) is given by: T=21.36-4.83xdelta(+ degrees )O(carb)-delta(+ degrees )O(wat) (T is in degrees C, delta(18)O(carb) is with respect to Vienna Pee Dee Belemnite (PDB), the International Atomic Energy Agency (IAEA) replacement standard for PDB, and delta(18)O(wat) is with respect to Vienna standard mean ocean water (VSMOW)) The outcome of the controlled experiment is compared with previous studies on synthetic, and biogenic, calcite and aragonite from field and laboratory investigations. These comparisons suggest that although a vital offset exists between the fractionation of isotopes in synthetic and biogenic aragonite for molluscs in general, there is no vital effect that is specific either to freshwater, or to individual, genera. Therefore, the calibrated relationship may be used for any freshwater or marine mollusc to derive palaeotemperatures providing the isotopic composition of the environmental water can be reliably constrained. Copyright 1999 John Wiley & Sons, Ltd.     

Effect of three-body forces on the lattice dynamics of noble metals

A simple method to generate an effective electron-ion interaction pseudopotential from the energy wave number characteristic obtained by first principles calculations has been suggested. This effective potential has been used, in third order perturbation, to study the effect of three-body forces on the lattice dynamics of noble metals. It is found that three-body forces, in these metals, do play an important role. The inclusion of such three-body forces appreciably improves the agreement between the experimental and theoretical phonon dispersion curves.     

Micro-Raman Spectroscopy and X-ray Diffraction Analyses of the Core and Shell Compartments of an Iron-Rich Fulgurite

Fulgurites are naturally occurring structures that are formed when lightning discharges reach the ground. In this investigation, the mineralogical compositions of core and shell compartments of a rare, iron-rich fulgurite from the Mongolian Gobi Desert were investigated by X-ray diffraction and micro-Raman spectroscopy. The interpretation of the Raman data was helped by chemometric analysis, using both multivariate curve resolution (MCR) and principal component analysis (PCA), which allowed for the fast identification of the minerals present in each region of the fulgurite. In the core of the fulgurite, quartz, microcline, albite, hematite, and barite were first identified based on the Raman spectroscopy and chemometrics analyses. In contrast, in the shell compartment of the fulgurite, the detected minerals were quartz, a mixture of the K-feldspars orthoclase and microcline, albite, hematite, and goethite. The Raman spectroscopy results were confirmed by X-ray diffraction analysis of powdered samples of the two fulgurite regions, and are consistent with infrared spectroscopy data, being also in agreement with the petrographic analysis of the fulgurite, including scanning electron microscopy with backscattering electrons (SEM-BSE) and scanning electron microscopy with energy dispersive X-ray (SEM-EDX) data. The observed differences in the mineralogical composition of the core and shell regions of the studied fulgurite can be explained by taking into account the effects of both the diffusion of the melted material to the periphery of the fulgurite following the lightning and the faster cooling at the external shell region, together with the differential properties of the various minerals. The heavier materials diffused slower, leading to the concentration in the core of the fulgurite of the iron and barium containing minerals, hematite, and barite. They first underwent subsequent partial transformation into goethite due to meteoric water within the shell of the fulgurite. The faster cooling of the shell region kinetically trapped orthoclase, while the slower cooling in the core area allowed for the extensive formation of microcline, a lower temperature polymorph of orthoclase, thus justifying the prevalence of microcline in the core and a mixture of the two polymorphs in the shell. The total amount of the K-feldspars decreases only slightly in the shell, while quartz and albite appeared in somewhat larger amounts in this compartment of the fulgurite. On the other hand, at the surface of the fulgurite, barite could not be stabilized due to sulfate lost (in the form of SO₂ plus O₂ gaseous products). The conjugation of the performed Raman spectroscopy experiments with the chemometrics analysis (PCA and, in particular, MCR analyses) was shown to allow for the fast identification of the minerals present in the two compartments (shell and core) of the sample. This way, the XRD experiments could be done while knowing in advance the minerals that were present in the samples, strongly facilitating the data analysis, which for compositionally complex samples, such as that studied in the present investigation, would have been very much challenging, if possible.