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).     

Tissue characterization using the continuous wavelet transform. Part II: Application on breast RF data

For pt.I see ibid., vol.48, no.2, p.356-63 (2001). In the first part of this work (Georgiou and Cohen 2000), a wavelet-based decomposition algorithm of the RF echo into its coherent and diffuse components was introduced. In this paper, the proposed algorithm is used to estimate structural parameters of the breast tissue such as the number and energy of coherent scatterers, the energy of the diffuse scatterers, and the correlation between them. Based on these individual parameters, breast tissue characterization is performed. The database used consists of 155 breast scans from 42 patients. The results are presented in terms of empirical receiver operating characteristics (ROC) curves. The results of this study are discussed in relation to the tissue microstructure. Individual estimated parameters are able to differentiate reliably between normal and fibroadenoma or fibrocystic or cancerous tissue (area under the ROC A_z>0.93). Also, the differentiation between malignant and benign (normal, fibrocystic, and fibroadenoma) tissue was possible (A_z>0.89)     

Measurement of optical transport properties of normal and malignant human breast tissue

We report measurement of optical transport parameters of normal and malignant (ductal carcinoma) human breast tissue. A spatially resolved steady-state diffuse reflectance technique was used for measurement of the reduced scattering coefficient (mu(s)?) and the absorption coefficient (mu(a)) of the tissue. The anisotropy parameter of scattering (g) was estimated by goniophotometric measurements of the scattering phase function. The values of mu(s)? and mu(a) for malignant breast tissue were observed to be larger than those for normal breast tissue over the wavelength region investigated (450-650 nm). Further, by using both the diffuse reflectance and the goniophotometric measurements, we estimated the Mie equivalent average radius of tissue scatterers to be larger in malignant tissue than in normal tissue.     

WOLD decomposition of the backscatter echo in ultrasound images of soft tissue organs

Deals with a method of detecting and estimating the scatterer spacing between the regularly spaced resolvable coherent scatterers in tissue. Scatterer spacing has been successfully used in classifying tissue structure, in differentiating between normal and cirrhotic liver, and in detecting diffuse liver disease. This paper presents a WOLD decomposition of the radio frequency (RF) field into its diffused and coherent components from which maximum likelihood estimates (MLE) or minimum mean square error (MMSE) estimates of the scattering spacing are easily computed. The MLE are efficient and for relatively long record are unbiased. They result in accurate estimates in low signal-to-noise (SNR) ratios. Unfortunately, they require nonlinear minimization and knowledge of the probability density associated with the RF backscatter echo. The MMSE estimates, on the other hand, are computationally simple, yield unique closed form solutions, do not require a-priori knowledge of the probability distribution function of the backscatter echo, and result in accurate estimates in low SNR ratios. This paper also presents an unbiased decision rule to detect whether or not an RF echo exhibits any specular scattering relative to the wavelength of the interrogating ultrasonic pulse. The approach has been tried on simulations as well as on in-vivo scans of liver data, and appears to perform well.     

Determination of optical parameters of human breast tissue from spatially resolved fluorescence: a diffusion theory model

We report the measurement of optical transport parameters of pathologically characterized malignant tissues, normal tissues, and different types of benign tumors of the human breast in the visible wavelength region. A spatially resolved steady-state diffuse fluorescence reflectance technique was used to estimate the values for the reduced-scattering coefficient (mu(s)') and the absorption coefficient (mu(a)) of human breast tissues at three wavelengths (530, 550, and 590 nm). Different breast tissues could be well differentiated from one another, and different benign tumors could also be distinguished by their measured transport parameters. A diffusion theory model was developed to describe fluorescence light energy distribution, especially its spatial variation in a turbid and multiply scattering medium such as human tissue. The validity of the model was checked with a Monte Carlo simulation and also with different tissue phantoms prepared with polystyrene microspheres as scatterers, riboflavin as fluorophores, and methylene blue as absorbers.     

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     

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.     

A feature parameter of optical diffuse reflectance on normal and malignant human breast tissue

Light that is delivered to the tissue surface undergoes multiple elastic scattering and absorption; part of it returns to the surface as optical diffuse reflectance, carrying quantitative information on the structure and composition of the measured tissue. In this paper, we utilized a well tested and publicly available Monte Carlo simulation software to simulate optical diffuse reflectance on normal and malignant human breast tissue in the visible wavelength region 450–650 nm. Based on the Monte Carlo simulation results, we discovered a feature parameter of optical diffuse reflectance on the simulated tissue surface. Normal and malignant human breast tissue may be discriminated by the value of the feature parameter. The values of the feature parameter are shown for normal and malignant human breast tissue in the visible wavelength region 450–650 nm. Experiments with tissue phantoms showed that the feature parameter is correlated to the component of the phantom. So the feature parameter is useful for the non-invasive optical diagnosis of biological tissue.     

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.     

Tissue characterization using the continuous wavelet transform. Part I: Decomposition method

In this paper, a novel decomposition of the RF ultrasound signal into its coherent and diffused components is proposed. This decomposition is based on thresholding the energy of the continuous wavelet transform of the RF signal using appropriate wavelets. The two components are modeled separately, and the model parameters are estimated. Previous work (Cohen et al. 1997) required assumptions about the periodicity of the coherent scatterers in the tissue. These assumptions are not necessary in this work. The decomposition algorithm is tested on simulated RF images. The accuracy of the estimated parameters is presented as well as the performance of the algorithm in low coherent-to-diffuse components' energy ratios (SNR)     

Maximum likelihood estimation of A-scan amplitudes for coherent targets in media of unresolvable scatterers

The author derives a maximum-likelihood estimator (MLE) for A-scan amplitudes corresponding to coherent reflectors embedded in media of unresolvable scatterers. The MLE processes sampled RF A-scans from broadband ultrasonic pulse-echo systems. A major source of interference for these signals is the backscattered energy from the unresolvable scatterers that exist throughout the beam field. A statistical model is formulated that characterizes the backscattered energy from a resolution cell when a coherent target scatterer is present. It is shown that the MLE is equivalent to a matched filter when the distribution of the interfering back-scatter energy is stationary over the resolution cell. In addition, the form of the MLE is described when the interfering echoes are not stationary within the resolution cell. Experimental results are presented for an adaptive implementation of the MLE applied to flaw detection in stainless steel. The results demonstrate the ability of the MLE to reveal targets masked by grain echoes, without prior knowledge of the gain-echo spectral characteristics.     

Spectral correlation in ultrasonic pulse echo signal processing

The effects of using spectral correlation in a maximum-likelihood estimator (MLE) for backscattered energy corresponding to coherent reflectors embedded in media of microstructure scatterers is considered. The spectral autocorrelation (SAC) function is analyzed for various scatterer configurations based on the regularity of the interspacing distance between scatterers. It is shown that increased regularity gives rise to significant spectral correlation, whereas uniform distribution of scatters throughout a resolution cell results in no significant correlation between spectral components. This implies that when a true uniform distribution for the effective scatterers exists, the power spectral density (PSD) is sufficient to characterize their echoes. However, as the microstructure scatterer distribution becomes more regular, SAC terms become more significant. MLE results for 15 A-scans from stainless steel specimens with three different grain sizes indicate an average 6-dB signal-to-noise ratio (SNR) improvement in the coherent scatterer (flat-bottom hole) echo intensities for estimators using the SAC characterization as opposed to the PSD characterization.     

Quantitative ultrasonic characterization of diffuse scatterers in the presence of structures that produce coherent echoes

Quantitative ultrasound (QUS) techniques that parameterize the backscattered power spectrum have demonstrated significant promise for ultrasonic tissue characterization. Some QUS parameters, such as the effective scatterer diameter (ESD), require the assumption that the examined medium contains uniform diffuse scatterers. Structures that invalidate this assumption can significantly affect the estimated QUS parameters and decrease performance when classifying disease. In this work, a method was developed to reduce the effects of echoes that invalidate the assumption of diffuse scattering. To accomplish this task, backscattered signal sections containing non-diffuse echoes were identified and removed from the QUS analysis. Parameters estimated from the generalized spectrum (GS) and the Rayleigh SNR parameter were compared for detecting data blocks with non-diffuse echoes. Simulations and experiments were used to evaluate the effectiveness of the method. Experiments consisted of estimating QUS parameters from spontaneous fibroadenomas in rats and from beef liver samples. Results indicated that the method was able to significantly reduce or eliminate the effects of nondiffuse echoes that might exist in the backscattered signal. For example, the average reduction in the relative standard deviation of ESD estimates from simulation, rat fibroadenomas, and beef liver samples were 13%, 30%, and 51%, respectively. The Rayleigh SNR parameter performed best at detecting nondiffuse echoes for the purpose of removing and reducing ESD bias and variance. The method provides a means to improve the diagnostic capabilities of QUS techniques by allowing separate analysis of diffuse and non-diffuse scatterers.     

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.     

On a Bayesian approach to coherent radar imaging

In coherent imaging the object of interest is complex but only its amplitude is to be estimated. The object phase yields nuisance variables and in a proper Bayesian approach it is necessary to obtain a phaseless likelihood function. We investigate a two-dimensional case in which the target object is modelled as a collection of point scatterers having independent random phases. The phaseless likelihood function is determined exactly for a configuration of data samples in a uniformly spaced square array in spatial frequency when the target scatterers are confined to lattice positions of a “matched” spatial array. It is determined approximately when the target scatterers are arbitrarily positioned, at most one per conventional resolution cell. The relation between maximum likelihood and conventional Fourier transform imaging is explored and the feasibility of a CLEAN algorithmic technique in coherent imaging is considered.©1993 John Wiley & Sons Inc     

Estimating mean scatterer spacing with the frequency-smoothedspectral autocorrelation function

The quasiperiodicity of regularly spaced scatterers results in characteristic patterns in the spectra of backscattered ultrasonic signals from which the mean scatterer spacing can be estimated. The mean spacing has been considered for classifying certain biological tissue. This paper addresses the problem of estimating the mean scatterer spacing from backscattered ultrasound signals using the frequency-smoothed spectral autocorrelation (SAC) function. The SAC function exploits characteristic differences between the phase spectrum of the resolvable quasiperiodic scatterers and the unresolvable uniformly distributed (diffuse) scatterers to improve estimator performance over other estimators that operate directly on the magnitude spectrum. Mean scatterer spacing estimates are compared for the frequency-smoothed SAC function and a cepstral technique using an AR model. Simulation results indicate that SAC-based estimates converge more reliably over smaller amounts of data than cepstrum-based estimates. An example of computing an estimate from liver tissue scans is also presented for the SAC function and the AR cepstrum     

Simplified inverse filter tracking algorithm for estimating the mean trabecular bone spacing

Ultrasonic backscatter signals provide useful information relevant to bone tissue characterization. Trabecular bone microstructures have been considered as quasi-periodic tissues with a collection of regular and diffuse scatterers. This paper investigates the potential of a novel technique using a simplified inverse filter tracking (SIFT) algorithm to estimate mean trabecular bone spacing (MTBS) from ultrasonic backscatter signals. In contrast to other frequency-based methods, the SIFT algorithm is a time-based method and utilizes the amplitude and phase information of backscatter echoes, thus retaining the advantages of both the autocorrelation and the cepstral analysis techniques. The SIFT algorithm was applied to backscatter signals from simulations, phantoms, and bovine trabeculae in vitro. The estimated MTBS results were compared with those of the autoregressive (AR) cepstrum and quadratic transformation (QT) . The SIFT estimates are better than the AR cepstrum estimates and are comparable with the QT values. The study demonstrates that the SIFT algorithm has the potential to be a reliable and robust method for the estimation of MTBS in the presence of a small signal-to-noise ratio, a large spacing variation between regular scatterers, and a large scattering strength ratio of diffuse scatterers to regular ones.     

Theoretical study of acousto-optical coherence tomography using random phase jumps on ultrasound and light

Acousto-optical coherence tomography (AOCT) is a variant of acousto-optic imaging (also called ultrasonic modulation imaging) that makes it possible to get the z resolution with acoustic and optic continuous wave beams. We describe here theoretically the AOCT effect, and we show that the acousto-optic "tagged photons" remain coherent if they are generated within a specific z region of the sample. We quantify the z selectivity for both the "tagged photon" field and for the Lesaffre et al. [Opt. Express 17, 18211 (2009)] photorefractive signal.     

Imaging through scattering media by the use of an analytical model of perturbation amplitudes in the time domain

A method of generating images through highly scattering media is presented that involves comparing measurements of the time-dependent intensity of transmitted light with an analytical model describing the sensitivity of that intensity on localized changes in optical properties. A least-squares fitting procedure is employed to derive the amplitudes of the measurement perturbations caused by embedded absorbers and scatterers located along a line of sight between the source and detector. Images are presented of a highly scattering, solid plastic phantom with optical properties closely matched to those of human breast tissue at near-infrared wavelengths. The phantom is a 54-mm-thick slab, containing four small cylinders of contrasting scatter and absorption. Results show that embedded absorbers can be distinguished from embedded scatterers, and that the diffusion perturbation amplitude provides inherently greater spatial resolution than the absorption perturbation amplitude.     

Optical slicing of human retinal tissue in vivo with the adaptive optics scanning laser ophthalmoscope

We present imaging results in human retinal tissue in vivo that allowed us to determine the axial resolution of the adaptive optics scanning laser ophthalmoscope (AOSLO). The instrument is briefly described, and the imaging results from human subjects are compared with (a) the estimated axial resolution values for a diffraction-limited, double-pass instrument and (b) the measured one for a calibrated diffuse retinal model. The comparison showed that the measured axial resolution, as obtained from optical sectioning of human retinas in vivo, can be as low as 71 microm for a 50 microm confocal pinhole after focusing a 3.5 mm beam with a 100 mm focal-length lens. The axial resolution values typically fall between the predictions from numerical models for diffuse and specular reflectors. This suggests that the reflection from the retinal blood vessel combines diffuse and specular components. This conclusion is supported by the almost universal interpretation that the image of a cylindrical blood vessel exhibits a bright reflection along its apex that is considered specular. The enhanced axial resolution achieved through use of adaptive optics leads to an improvement in the volume resolution of almost 2 orders of magnitude when compared with a conventional scanning laser ophthalmoscope and almost a factor of 3 better than commercially available optical coherence tomographic instruments.