Bayesian 2-D deconvolution: a model for diffuse ultrasound scattering

Observed medical ultrasound images are degraded representations of the true acoustic tissue reflectance. The degradation is due to blur and speckle and significantly reduces the diagnostic value of the images. To remove both blur and speckle, we have developed a new statistical model for diffuse scattering in 2-D ultrasound radio frequency images, incorporating both spatial smoothness constraints and a physical model for diffuse scattering. The modeling approach is Bayesian in nature, and we use Markov chain Monte Carlo methods to obtain the restorations. The results from restorations of some real and simulated radio frequency ultrasound images are presented and compared with results produced by Wiener filtering     

Bayesian 2-D deconvolution: effect of using spatially invariant ultrasound point spread functions

Observed ultrasound images are degraded representations of the true tissue reflectance. The specular reflections at boundaries between regions of different tissue types are blurred, and the diffuse scattering within homogenous regions causes speckle because of the oscillating nature of the transmitted pulse. To reduce both blur and speckle, we have developed algorithms for the restoration of simulated and real ultrasound images based on Markov random field models and Bayesian statistical methods. The algorithm is summarized here. Because the point spread function (psf) is unknown, we investigate the effects of using incorrect frequencies and sizes for the model psf during the restoration process. First, we degrade the images either with a known simulated psf or a measured psf. Then, we use different psf shapes during restoration to study the robustness of the method. We found that small variations in the parameters characterizing the psf, less than ±25% change in frequency, width, or length, still yielded satisfactory results. When altering the psf more than this, the restorations were not acceptable. The restorations were particularly sensitive to large increases in the restoring psf frequency. Thus, 2-D Bayesian restoration using a fixed psf may yield acceptable results as long as the true variant psfs have not varied too much during imaging     

存在镜面反射时的双目立体匹配

传统的立体匹配方法建立在Lambertian的漫反射模型之上,漫反射模型的立体匹配在一个图像的大多部分是有效的,但是在处理图像中包含镜面反射的部分时结果会产生严重的匹配错误。笔者利用漫反射和镜面反射在灰度和最大色度上的不同,分离出镜面反射的像素,然后采用一种针对镜面反射的匹配测度,在图像中漫反射部分和镜面反射部分都能匹配得到正确的视差。结果证明了方法的有效性。     

Statistical characterization of diffuse scattering in ultrasound images

The marginal statistics for the diffused ultrasound speckle echo has been postulated as exhibiting circularly symmetric Gaussian behavior similar to the laser speckle for monochromatic illumination under the assumption of a large number of unresolvable scatterers per resolution cell. This is known in the literature as the Rayleigh scattering condition. This paper presents a formal statistical test, the Kolmogorov-Smirnov nonparametric goodness of fit statistical test, to test the hypothesis that the unresolvable part (diffuse part) of the backscatter echo follows a Rayleigh scattering condition, and obtain numerical values for the scatterer concentration required for the Rayleigh condition to be valid. In addition, it presents a formal statistical test, the Kolmogorov-Smirnov nonparametric homogeneity statistical test, to compare two regions of interest with different scattering concentrations without prior knowledge of the nature of the scattering conditions (Rayleigh or non-Rayleigh scattering). Unlike all previous parametric testing methods that treat the A-scan or B-scan echo as a random sample, the authors' method presents formal tests based on the colored nature of the diffuse backscattered echo which is a more realistic model of the diffuse scattering component. The tests are demonstrated on simulations of RF scans with different scatterer concentrations per resolution cell as well as on phantom data which mimic tissue.     

Ultrasound speckle reduction using harmonic oscillator models

A speckle reduction algorithm called the harmonic imaging (HI) algorithm is presented. It is based on a multicomponent scattering model for medical ultrasonics. The backscattered ultrasound quadrature signal is modeled as the sum of three components after demodulation. The first component represents nonresolvable diffuse scatterers, while the second component represents subresolvable quasi-periodic scatterers. The third component represents resolvable quasi-periodic scatterers and mirroring surfaces. Since the second component gives rise to the most long range destructive interference effects it is eliminated in the HI algorithm to reduce speckle. Due to its slow spatial variation, it can be almost completely eliminated simply by differentiating the backscattered demodulated quadrature signal. Lissajous-like figures are observed in complex plots of the signals from ultrasound beams going through tissues with quasi-periodic components and sometimes in areas with only diffuse scatterers. Therefore the sum of the complex signals from the resolvable and nonresolvable scatterers within a resolution cell is modeled by two orthogonal and independent harmonic oscillators. The estimated, total energy of these two oscillators determines the gray level value of the HI image within the resolution cell. The HI images produced using radio frequency data from a phantom and from tissues in vivo are more blurred than ordinary envelope images, but the signal to noise ratio and tissue contrast were higher for the HI images     

Wavelet restoration of medical pulse-echo ultrasound images in an EM framework

The clinical utility of pulse-echo ultrasound images is severely limited by inherent poor resolution that impacts negatively on their diagnostic potential. Research into the enhancement of image quality has mostly been concentrated in the areas of blind image restoration and speckle removal, with little regard for accurate modeling of the underlying tissue reflectivity that is imaged. The acoustic response of soft biological tissues has statistics that differ substantially from the natural images considered in mainstream image processing: although, on a macroscopic scale, the overall tissue echogenicity does behave some-what like a natural image and varies piecewise-smoothly, on a microscopic scale, the tissue reflectivity exhibits a pseudo-random texture (manifested in the amplitude image as speckle) due to the dense concentrations of small, weakly scattering particles. Recognizing that this pseudorandom texture is diagnostically important for tissue identification, we propose modeling tissue reflectivity as the product of a piecewise-smooth echogenicity map and a field of uncorrelated, identically distributed random variables. We demonstrate how this model of tissue reflectivity can be exploited in an expectation-maximization (EM) algorithm that simultaneously solves the image restoration problem and the speckle removal problem by iteratively alternating between Wiener filtering (to solve for the tissue reflectivity) and wavelet-based denoising (to solve for the echogenicity map). Our simulation and in vitro results indicate that our EM algorithm is capable of producing restored images that have better image quality and greater fidelity to the true tissue reflectivity than other restoration techniques based on simpler regularizing constraints.     

3D reconstruction of concave surfaces using polarisation imaging

This paper presents a novel algorithm for improved shape recovery using polarisation-based photometric stereo. The majority of previous research using photometric stereo involves 3D reconstruction using both the diffuse and specular components of light; however, this paper suggests the use of the specular component only as it is the only form of light that comes directly off the surface without subsurface scattering or interreflections. Experiments were carried out on both real and synthetic surfaces. Real images were obtained using a polarisation-based photometric stereo device while synthetic images were generated using PovRay® software. The results clearly demonstrate that the proposed method can extract three-dimensional (3D) surface information effectively even for concave surfaces with complex texture and surface reflectance.     

Ultrasound Speckle Reduction Based on Histogram Curve Matching and Region Growing

The quality of ultrasound scanning images is usually damaged by speckle noise. This paper proposes a method based on local statistics extracted from a histogram to reduce ultrasound speckle through a region growing algorithm. Unlike single statistical moment-based speckle reduction algorithms, this method adaptively smooths the speckle regions while preserving the margin and tissue structure to achieve high detectability. The criterion of a speckle region is defined by the similarity value obtained by matching the histogram of the current processing window and the reference window derived from the speckle region in advance. Then, according to the similarity value and tissue characteristics, the entire image is divided into several levels of speckle-content regions, and adaptive smoothing is performed based on these classification characteristics and the corresponding window size determined by the proposed region growing technique. Tests conducted from phantoms and in vivo images have shown very promising results after a quantitative and qualitative comparison with existing work.     

基于光源平移恢复物体法线和材质的算法

提出了一种基于光源平移恢复物体法线和材质的算法.光源平移时获得一组输入图像.根据输入图像将物体表面上的点分成纯漫反射点和混合点(包含漫反射和镜面反射的点).首先,根据镜面反射的原理求出混合点的法线.然后根据求出的法线用全局优化的迭代方法来恢复物体的材质.最后,根据不同输入图像中光源与物体的相对位置的不同,通过一个三角函数来恢复物体表面纯漫反射点的法线.分析对比实验结果和场景的真实参数表明,算法能够有效地恢复物体的法线和材质.     

Post-beamforming second-order Volterra filter for pulse-echo ultrasonic imaging

We present a new algorithm for deriving a second-order Volterra filter (SVF) capable of separating linear and quadratic components from echo signals. Images based on the quadratic components are shown to provide contrast enhancement between tissue and ultrasound contrast agents (UCAs) without loss in spatial resolution. It is also shown that the quadratic images preserve the low scattering regions due to their high dynamic range when compared with standard B-mode or harmonic images. A robust algorithm for deriving the filter has been developed and tested on real-time imaging data from contrast and tissue-mimicking media. Illustrative examples from image targets containing contrast agent and tissue-mimicking media are presented and discussed. Quantitative assessment of the contrast enhancement is performed on both the RF data and the envelope-detected log-compressed image data. It is shown that the quadratic images offer levels of enhancement comparable or exceeding those from harmonic filters while maintaining the visibility of low scattering regions of the image.     

Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis

The Monte Carlo-based inverse model of diffuse reflectance described in part I of this pair of companion papers was applied to the diffuse reflectance spectra of a set of 17 malignant and 24 normal-benign ex vivo human breast tissue samples. This model allows extraction of physically meaningful tissue parameters, which include the concentration of absorbers and the size and density of scatterers present in tissue. It was assumed that intrinsic absorption could be attributed to oxygenated and deoxygenated hemoglobin and beta-carotene, that scattering could be modeled by spheres of a uniform size distribution, and that the refractive indices of the spheres and the surrounding medium are known. The tissue diffuse reflectance spectra were evaluated over a wavelength range of 400-600 nm. The extracted parameters that showed the statistically most significant differences between malignant and nonmalignant breast tissues were hemoglobin saturation and the mean reduced scattering coefficient. Malignant tissues showed decreased hemoglobin saturation and an increased mean reduced scattering coefficient compared with nonmalignant tissues. A support vector machine classification algorithm was then used to classify a sample as malignant or nonmalignant based on these two extracted parameters and produced a cross-validated sensitivity and specificity of 82% and 92%, respectively.     

Unsupervised segmentation of RF echo into regions with different scattering characteristics

Recent experimental results verify that the probability distribution function of the diffuse component of the RF echo depends primarily on the concentration of the diffuse scatterers in the resolution cell. In this paper we apply these results to develop an unsupervised segmentation scheme that partitions an RF A-scan or B-scan image into statistically homogeneous regions that reflect the underlying scattering characteristics. The proposed segmentation scheme is based on a nonparametric homogeneity test that compares two regions of interest (ROI) for possible merging utilizing information about both the coherent and the diffuse component of the RF echo. For the coherent component, homogeneity is defined in terms of the estimated average spacing of each ROI. For the diffuse component, we use the nonparametric Kolmogorov-Smirnov (K-S) homogeneity statistical test that compares two empirical distributions associated with any two ROIs. This test can be used to obtain a segmentation into regions with different scattering characteristics regardless of the nature of the scattering conditions (e.g., Rayleigh regions with different scatterer concentration, different non-Rayleigh regions, or different coherent scattering regions). Finer segmentation can be obtained by learning the distributions associated with the various homogeneous regions obtained from the coarse segmenter. The proposed segmentation scheme is applied on simulated RF scans with different scatterer concentration per resolution cell, on phantom data which mimic tissue, and on liver scans. The results demonstrate the effectiveness of the segmentation algorithm even in cases of subtle differences in the scattering characteristics of each region (for example, diffuse component with scatterer density of 16 and 32 scatterers per resolution cell).     

Maximum likelihood segmentation of ultrasound images with Rayleigh distribution

This study presents a geometric model and a computational algorithm for segmentation of ultrasound images. A partial differential equation (PDE)-based flow is designed in order to achieve a maximum likelihood segmentation of the target in the scene. The flow is derived as the steepest descent of an energy functional taking into account the density probability distribution of the gray levels of the image as well as smoothness constraints. To model gray level behavior of ultrasound images, the classic Rayleigh probability distribution is considered. The steady state of the flow presents a maximum likelihood segmentation of the target. A finite difference approximation of the flow is derived, and numerical experiments are provided. Results are presented on ultrasound medical images as fetal echography and echocardiography.     

Modeling the bidirectional reflectance of emissive displays

The reflection properties of a display device influence the available contrast and affect the perception of subtle detail. The display reflection characteristics of flat-panel displays (FPDs) are appropriately described by a six-dimensional bidirectional reflectance distribution function (BRDF). I describe a Monte Carlo method for modeling the bidirectional reflectance of multilayer emissive structures used in electronic display devices. I estimate the complete BRDF using a one-dimensional angular distribution function of the luminance. I apply the method to model typical high-performance cathode-ray tube and FPD structures. I find that, for the BRDF signatures of cathode-ray tubes characterized by a specular and a quasi-Lambertian components, the estimated values for the specular and diffuse reflection coefficients agree well with low-resolution experimental measurements conducted with a rotation arm and a collimated probe. I show that emissive FPDs with thin-film organic layers on reflective substrates can exhibit a predominant specular peak broadened by short-range light scattering.     

Infrared reflection-absorption spectra of metal-effect coatings

The results of studies of infrared reflection-absorption spectra of metal-effect coatings are presented in this paper. Such coatings consist of metallic flakes that are dispersed in a polymer binder. The spectra show two distinct phenomena. One is due to the polymer matrix. The other is due to metallic flakes that are dispersed inside the layer. The polymer binder causes narrow spectral lines that give a thickness-dependent intensity and position. Metallic flakes change the average baseline of this spectrum over the entire infrared spectral region. This particular effect was evaluated using a simple rough-surface model. Two parameters of the model, the root-mean-square roughness and the correlation length of the rough surface, described the reflection of the partial beams on the metal flake surfaces and scattering on flakes boundaries. The other two parameters are the specular reflectance and the diffuse reflectance of the plane untextured interface between the polymer matrix and the metal flake surface. Various metal-effect coatings within the same polymer binder were analyzed. The effect of each metal flake dispersion was evaluated by the parameters within the rough-surface model. The results were analyzed in terms of the size and the loadings of flakes that were used in the coatings.     

Variational estimation of inhomogeneous specular reflectance and illumination from a single view

Estimating the illumination and the reflectance properties of an object surface from a few images is an important but challenging problem. The problem becomes even more challenging if we wish to deal with real-world objects that naturally have spatially inhomogeneous reflectance. In this paper, we derive a novel method for estimating the spatially varying specular reflectance properties of a surface of known geometry as well as the illumination distribution of a scene from a specular-only image, for instance, recovered from two images captured with a polarizer to separate reflection components. Unlike previous work, we do not assume the illumination to be a single point light source. We model specular reflection with a spherical statistical distribution and encode its spatial variation with a radial basis function (RBF) network of their parameter values, which allows us to formulate the simultaneous estimation of spatially varying specular reflectance and illumination as a constrained optimization based on the I-divergence measure. To solve it, we derive a variational algorithm based on the expectation maximization principle. At the same time, we estimate optimal encoding of the specular reflectance properties by learning the number, centers, and widths of the RBF hidden units. We demonstrate the effectiveness of the method on images of synthetic and real-world objects.     

Fundamental correlation lengths of coherent speckle in medical ultrasonic images

Refinements to previous analyses of the natural correlation lengths within simple images and between images to be compounded are presented. Comparison of theoretical and experimental results show very good agreement for the case of Rayleigh scattering media: the correlation length within a simple image is comparable to the resolution cell size; the correlation length between images to be spatially compounded is comparable to, but smaller than, the transducer on array aperture; and the correlation length between images to be frequency-compounded becomes a frequency comparable to their bandwidth. Complications arising from the presence of specular scattering or due to the presence of just a few scatterers are considered. It is shown that straightforward solutions exist for either of these problems taken by itself. When they occur in combination, calibration techniques may lead to unambiguous identification of the contributions to the scattering from diffuse or incoherent scattering and from specular or coherent scattering, and to estimation of the density of diffuse scatterers.     

Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates method

Here light propagation and radiation transfer of ultrafast laser pulses in heterogeneous biological tissues are simulated by use of the discrete-ordinates method (DOM). Formulations for solving the time-dependent radiation-transfer equation are deduced for three-dimensional geometries incorporating the Fresnel specularly reflecting boundary condition and characteristics of ultrafast laser pulses. The present method can treat both the incident laser intensity and the scattered radiation intensity from the walls of the targeted tissue as two components, i.e., a diffuse part and a specular part. Reflectivity at the tissue-air interface is calculated by use of Snell's law and the Fresnel equation. The high-order S10 DOM method is found to be adequate for describing the propagation and transfer of ultrafast laser radiation in heterogeneous tissues. The time-dependent radiation field in the tissue as well as the temporal radiation intensity profiles at the boundaries can be obtained simultaneously. The absolute values of the logarithmic slope of the temporal reflectance and transmittance at various detector positions are found to converge to a constant value in a homogeneous tissue model. With the inclusion of a small inhomogeneity, such a value will change in line with the property of the embedded inhomogeneity. The orientation of heterogeneity of the tissues also substantially affects the radiation intensity at the boundaries. The effect of the Fresnel boundary in the modeling is pronounced. The simulated transmitted signals are broadened and amplified under specularly reflecting boundary condition as compared with those under diffusely reflecting boundary conditions.     

Sensitivity of high vacuum standard parameters to the share of molecule specular reflections in the gas scattering

The molecular gas flow parameters were evaluated using cosine form of the scattering function of the molecules incident on the surface. This gas scattering model is commonly used for calculating the vacuum system parameters, but it is theoretically valid only if the vacuum system is in equilibrium. This also means that there is no flow in the system. We applied the Maxwell's model of gas scattering with the contribution of specular reflections to study how these reflections influence the flow parameters. In typical calibration systems with dynamic expansion of gases, a 10% contribution of the specular reflections results in the 0.18% decrease of the computed value of the gas density inside the gauge to be calibrated as compared with that when the cosine law is employed.     

Hemispherical and diffuse reflectance and transmittance of a slightly inhomogeneous film bounded by rough, unparallel interfaces

The optical reflectance and transmittance of an ideal thin film are calculated in a well-known way. As far as a non-ideal thin film is concerned - i.e., a slightly inhomogeneous thin film bounded by rough, unparallel interfaces - three categories of spectral coefficients can be defined, i.e.: specular reflectance and direct transmittance (light intensity flux along the optical axis), hemispherical reflectance and transmittance (light intensity flux integrated over the solid half angle π), and diffuse reflectance and transmittance (light intensity flux scattered around the optical axis) coefficients. In this paper a model recently introduced for the specular and direct coefficients is generalized to calculate also the hemispherical and diffuse coefficients of a non-ideal film.