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     

Superresolution of ultrasound images using the first and second harmonic signal

This paper presents a new method of blind two-dimensional (2-D) homomorphic deconvolution and speckle reduction applied to medical ultrasound images. The deconvolution technique is based on an improved 2-D phase unwrapping scheme for pulse estimation. The input images are decomposed into minimum-phase and allpass components. The 2-D phase unwrapping is applied only to the allpass component. The 2-D phase of the minimum-phase component is derived by a Hilbert transform. The accuracy of 2-D phase unwrapping is also improved by processing small (16 x 16 pixels) overlapping subimages separately. This takes the spatial variance of the ultrasound pulse into account. The deconvolution algorithm is applied separately to the first and second harmonic images, producing much sharper images of approximately the same resolution and different speckle patterns. Speckle reduction is made by adding the envelope images of the deconvolved first and second harmonic images. Neither the spatial resolution nor the frame rate decreases, as the common compounding speckle reduction techniques do. The method is tested on sequences of clinical ultrasound images, resulting in high-resolution ultrasound images with reduced speckle noise.     

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.     

Intervening attenuation affects first-order statistical properties of ultrasound echo signals

Previous studies show that first-order statistical properties of ultrasound echo signals are related to the effective number of scatterers in the "resolution cell" of a pulse-echo ultrasound system. When the effective number of scatterers is large (~10 or more) this results in echo signals whose amplitude follows a Rayleigh distribution, with the RF echo signal obeying Gaussian statistics; deviation from Rayleigh or Gaussian statistics yields information on scatterer number densities. In this paper, the influence of the medium's attenuation on non-Gaussian properties of the echo signal is considered. Preferential attenuation of higher frequency components of a pulsed ultrasound beam effectively broadens the beam and increases the resolution cell size. Thus, the resultant non-Gaussian parameter for broad bandwidth excitation of the transducer depends not only on the scatterer number density but also on the attenuation in the medium. These effects can be reduced or eliminated by using narrow-band experiments.     

Capon beamforming in medical ultrasound imaging with focused beams

Medical ultrasound imaging is conventionally done by insonifying the imaged medium with focused beams. The backscattered echoes are beamformed using delay-and-sum operations that cannot completely eliminate the contribution of signals backscattered by structures off the imaging beam to the beamsum. It leads to images with limited resolution and contrast. This paper presents an adaptation of the Capon beamformer algorithm to ultrasound medical imaging with focused beams. The strategy is to apply data-dependent weight functions to the imaging aperture. These weights act as lateral spatial filters that filter out off-axis signals. The weights are computed for each point in the imaged medium, from the statistical analysis of the signals backscattered by that point to the different elements of the imaging probe when insonifying it with different focused beams. Phantom and in vivo images are presented to illustrate the benefits of the Capon algorithm over the conventional delay and-sum approach. On heart sector images, the clutter in the heart chambers is decreased. The endocardium border is better defined. On abdominal linear array images, significant contrast and resolution enhancement are observed.     

Real-time ultrasound simulation using the GPU

Ultrasound simulators can be used for training ultrasound image acquisition and interpretation. In such simulators, synthetic ultrasound images must be generated in real time. Anatomy can be modeled by computed tomography (CT). Shadows can be calculated by combining reflection coefficients and depth dependent, exponential attenuation. To include speckle, a pre-calculated texture map is typically added. Dynamic objects must be simulated separately. We propose to increase the speckle realism and allow for dynamic objects by using a physical model of the underlying scattering process. The model is based on convolution of the point spread function (PSF) of the ultrasound scanner with a scatterer distribution. The challenge is that the typical field-of-view contains millions of scatterers which must be selected by a virtual probe from an even larger body of scatterers. The main idea of this paper is to select and sample scatterers in parallel on the graphic processing unit (GPU). The method was used to image a cyst phantom and a movable needle. Speckle images were produced in real time (more than 10 frames per second) on a standard GPU. The ultrasound images were visually similar to images calculated by a reference method.     

The effect of including myocardial anisotropy in simulated ultrasound images of the heart

We have examined the effect of incorporating tissue anisotropy in simulated ultrasound images of the heart. In simulation studies, the cardiac muscle (myocardium) is usually modeled as a cloud of uncorrelated point scatterers. Although this approach successfully generates a realistic speckle pattern, it fails to reproduce any effects of image anisotropy seen in real ultrasound images. We hypothesize that some of this effect is caused by the varying orientation of anisotropic myocardial structures relative to the ultrasonic beam and that this can be taken into account in simulations by imposing an angle dependent correlation of the scatterer points. Ultrasound images of a porcine heart were obtained in vitro, and the dominating fiber directions were estimated from the insonification angles that gave rise to the highest backscatter intensities. A cylindrical sample of the myocardium was then modeled as a grid of point scatterers correlated in the principal directions of the muscle fibers, as determined experimentally. Ultrasound images of the model were simulated by using a fast k-space based convolution approach, and the results were compared with the in vitro recordings. The simulated images successfully reproduced the insonification dependent through-wall distribution of backscatter intensities in the myocardial sample, as well as a realistic speckle pattern.     

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.     

Modeling and analysis of ultrasound backscattering by spherical aggregates and rouleaux of red blood cells

The present study concerns the modeling and analysis of ultrasound backscattering by red blood cell (RBC) aggregates, which under pathological conditions play a significant role in the rheology of blood within human vessels. A theoretical model based on the convolution between a tissue matrix and a point spread function, representing, respectively, the RBC aggregates and the characteristics of the ultrasound system, was used to examine the influence of the scatterer shape and size on the backscattered power. Both scatterers in the form of clumps of RBC aggregates and rouleaux were modeled. For all simulations, the hematocrit was kept constant at 10%, the ultrasound frequency was 10 MHz, the insonification angle was varied from 0 to 90 degrees , and the scatterer size (diameter for clumps and length for rouleaux) ranged from 4 mum to 120 mum. Under Rayleigh scattering by assuming a Poisson distribution of scatterers in space, the ultrasound backscattered power increased linearly with the particle volume. For non-Rayleigh scatterers, the intensity of the echoes diminished as the scatterer volume increased, with the exception of rouleaux at an angle of 90 degrees . As expected, the backscattered power was angularly dependent for anisotropic particles (rouleaux). The ultrasound backscattered power did not always increase with the size of the aggregates, especially when they were no longer Rayleigh scatterers. In the case of rouleaux, the anisotropy of the backscattered power is emphasized in the non-Rayleigh region.     

Tissue stiffness imaging method using temporal variation of ultrasound speckle pattern

Applying vibration to a medium makes it vibrate. The resulting change in scatterer distribution inside the medium due to applied vibration changes the speckle pattern of ultrasound images. In this case, scatterers in a hard medium experience small displacements, and those in a soft medium experience large displacements. As a result, the amount of speckle pattern brightness change in ultrasound images is related to the tissue stiffness. Using this dependency, a two-dimensional profile of relative tissue stiffness can be constructed qualitatively at the display pixel resolution by determining at each pixel the standard deviation and/or the difference between minimum and maximum values over a certain number of consecutive B-mode images. Experiments with phantoms show that the softer the tissue, the larger the standard deviation. The proposed imaging modality is a simple yet practical method of resolving hard cysts surrounded by soft background in a phantom using B-mode frame data only.     

Speckle decorrelation due to two-dimensional flow gradients

The performance of ultrasonic velocity estimation methods is degraded by speckle decorrelation, the change in received echoes over time. Because ultrasonic speckle is formed by the complex sum of echoes from subresolution scatterers, it is sensitive to the relative motion of those scatterers. Velocity gradients in flowing blood result in relative scatterer motion and can be a significant source of speckle decorrelation. Computer simulations were performed to evaluate speckle decorrelation due to two-dimensional flow gradients. Results indicate that decorrelation due to flow gradients is sensitive to the angle of flow and has a maximum at a beam-vessel angle of 0 degrees , i.e., purely axial flow. A quantitative summary of the major factors causing speckle decorrelation indicates that flow gradients are the most significant contributors under the conditions modeled.     

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.     

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)     

Continuous wave ultrasonic tomography

As an object rotates with respect to a stationary ultrasonic beam, the scattering centers within the object return echoes that are Doppler-shifted in frequency by amounts depending on the velocities of the individual scatterers. The scattering centers that lie on a line of constant cross-range all have the same effective velocity in the direction pointing toward the transducer; therefore, the backscattered echo amplitude at any particular frequency is the line integral of the scattered radiation at the cross-range corresponding to that frequency. The amplitudes of the returned signals at other frequencies give the line integrals for the scatterers at the corresponding cross-ranges. The amplitude as a function of frequency can be interpreted as a tomographic projection. A continuum of the projections at different positions is generated while the object is rotating. A tomographic reconstruction algorithm can produce an image of the distribution of scattering centers in the insonified object from these projections. A microscanner was developed to investigate the approach of using continuous wave (CW) ultrasound for cross-sectional imaging. The resolution is limited by the target size and the ultrasonic wavelength.     

Markov models of specular and diffuse scattering in restoration ofmedical ultrasound images

Observed medical 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 such regions also contains speckle. This reduces the diagnostic value of such images. In order to remove both blur and speckle, the authors develop a maximum a posteriori deconvolution algorithm for two-dimensional (2-D) ultrasound radio frequency (RF) images based on a new Markov random field image model incorporating spatial smoothness constraints and physical models for specular reflections and diffuse scattering. During stochastic relaxation, the algorithm alternates steps of restoration and segmentation, and includes estimation of reflectance parameters. The smoothness constraints regularize the overall procedure, and the algorithm uses the specular reflection model to locate region boundaries. The resulting restorations of some simulated and real RF images are significantly better than those produced by Wiener filtering     

High-resolution ultrasonic imaging using fast two-dimensional homomorphic filtering.

A new method for two-dimensional deconvolution of medical ultrasonic images is presented. The spatial resolution of the deconvolved images is much higher compared to the common images of the fundamental and second harmonic. The deconvolution also results in a more distinct speckle pattern. Unlike the most published deconvolution algorithms for ultrasonic images, the presented technique can be implemented using currently available hardware in real-time imaging, with a rate up to 50 frames per second. This makes it attractive for application in the current ultrasound scanners. The algorithm is based on two-dimensional homomorphic deconvolution with simplified assumptions about the point spread function. Broadband radio frequency image data are deconvolved instead of common fundamental harmonic data. Thus, information of both the first and second harmonics is used. The method was validated on image data recorded from a tissue-mimicking phantom and on clinical image data.     

High-resolution ultrasonic imaging using two-dimensional homomorphic filtering

A new method for two-dimensional deconvolution of medical ultrasonic images is presented. The spatial resolution of the deconvolved images is much higher compared to the common images of the fundamental and second harmonic. The deconvolution also results in a more distinct speckle pattern. Unlike the most published deconvolution algorithms for ultrasonic images, the presented technique can be implemented using currently available hardware in real-time imaging, with a rate up to 50 frames per second. This makes it attractive for application in the current ultrasound scanners. The algorithm is based on two-dimensional homomorphic deconvolution with simplified assumptions about the point spread function. Broadband radio frequency image data are deconvolved instead of common fundamental harmonic data. Thus, information of both the first and second harmonics is used. The method was validated on image data recorded from a tissue-mimicking phantom and on clinical image data.     

Modeling ultrasound echoes in skin tissues using symmetric α-stable processes

Starting from the widely accepted point-scattering model, this paper establishes, through analytical developments, that ultrasound signals backscattered from skin tissues converge to a complex Levy flight random process with non- Gaussian α-stable statistics. The envelope signal follows a generalized (heavy-tailed) Rayleigh distribution. It is shown that these signal statistics imply that scatterers have heavy-tailed power-law cross sections. This model generalizes the Gaussian framework and provides a formal representation for a new case of non-Gaussian statistics, in which both the number of scatterers and the variance of their cross sections tend to infinity. In addition, analytical expressions are derived to relate the α-stable parameters to scatterer properties. Simulations show that these expressions can be used as rigorous interpretation tools for tissue characterization. Several experimental results supported by excellent goodness-of-fit tests confirm the proposed analytical model. Finally, these fundamental results set the basis for new echography processing methods and quantitative ultrasound characterization tools.     

Computer model for harmonic ultrasound imaging

Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. Here, the authors present a computer model that can generate realistic harmonic images. In this model, the incident ultrasound is modeled after the "KZK" equation, and the echo signal is modeled using linear propagation theory because the echo signal is much weaker than the incident pulse. Both time domain and frequency domain numerical solutions to the "KZK" equation were studied. Realistic harmonic images of spherical lesion phantoms were generated for scans by a circular transducer. This model can be a very useful tool for studying the harmonic buildup and dissipation processes in a nonlinear medium, and it can be used to investigate a wide variety of topics related to B-mode harmonic imaging.     

Computer model for harmonic ultrasound imaging

Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. In this paper, we present a computer model that can generate realistic harmonic images. In this model, the incident ultrasound is modeled after the "KZK" equation, and the echo signal is modeled using linear propagation theory because the echo signal is much weaker than the incident pulse. Both time domain and frequency domain numerical solutions to the "KZK" equation were studied. Realistic harmonic images of spherical lesion phantoms were generated for scans by a circular transducer. This model can be a very useful tool for studying the harmonic buildup and dissipation processes in a nonlinear medium, and it can be used to investigate a wide variety of topics related to B-mode harmonic imaging.