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

Carotid artery ultrasound image analysis: A review of the literature

Stroke is one of the prominent causes of death in the recent days. The existence of susceptible plaque in the carotid artery can be used in ascertaining the possibilities of cardiovascular diseases and long-term disabilities. The imaging modality used for early screening of the disease is B-mode ultrasound image of the person in the artery area. The objective of this article is to give a widespread review of the imaging modes and methods used for studying the carotid artery for identifying stroke, atherosclerosis and related cardiovascular diseases. We encompass the review in methods used for artery wall tracking, intima-media, and lumen segmentation which will help in finding the extent of the disease. Due to the characteristics of the imaging modality used, the images have speckle noise which worsens the image quality. Adaptive homomorphic filtering with wavelet and contourlet transforms, Levy Shrink, gamma distribution were used for image denoising. Learning-based neural network approaches for denoising give better edge preservation. Domain knowledge-based segmentation approaches have proved to provide more accurate intima-media thickness measurements. There is a requirement of useful fully automatic segmentation approaches, 3D, 4D systems, and plaque motion analysis. Taking into consideration the image priors like geometry, imaging physics, intensity and temporal data, image analysis has to be performed. Encouragingly more research has focused on content-specific segmentation and classification techniques. With the evaluation of machine learning algorithms, classifying the image as with or without a fat deposit has gained better accuracy and sensitivity. Machine learning-based approaches like self-organizing map, k-nearest neighborhood and support vector machine achieve promising accuracy and sensitivity in classification. The literature reveals that there is more scope in identifying a patient-specific model in a fully automatic manner.

Estimating blood vessel areas in ultrasound images using a deformable template model

We consider the problem of obtaining interval estimates of vessel areas from ultrasound images of cross sections through the carotid artery. Robust and automatic estimates of the cross sectional area is of medical interest and of help in diagnosing atherosclerosis, which is caused by plaque deposits in the carotid artery. We approach this problem by using a deformable template to model the blood vessel outline, and use recent developments in ultrasound science to model the likelihood. We demonstrate that by using an explicit model for the outline, we can easily adjust for an important feature in the data: strong edge reflections called specular reflection. The posterior is challenging to explore, and naive standard MCMC algorithms simply converge too slowly. To obtain an efficient MCMC algorithm we make extensive use of computational efficient Gaussian Markov random fields, and use various block sampling constructions that jointly update large parts of the model.

Sparsity driven ultrasound imaging

An image formation framework for ultrasound imaging from synthetic transducer arrays based on sparsity-driven regularization functionals using single-frequency Fourier domain data is proposed. The framework involves the use of a physics-based forward model of the ultrasound observation process, the formulation of image formation as the solution of an associated optimization problem, and the solution of that problem through efficient numerical algorithms. The sparsity-driven, model-based approach estimates a complex-valued reflectivity field and preserves physical features in the scene while suppressing spurious artifacts. It also provides robust reconstructions in the case of sparse and reduced observation apertures. The effectiveness of the proposed imaging strategy is demonstrated using experimental data.

Estimation of average speed of sound using deconvolution of medical ultrasound data

In diagnostic ultrasound imaging the speed of sound is assumed to be 1540 m/s in soft tissues. When the actual speed is different, the mismatch can lead to distortions in the acquired images and so reduce their clinical value. Therefore, the estimation of the true speed has been pursued not only because it enables image correction but also as a way of tissue characterisation. In this article, we present a novel way to measure the average speed of sound concurrently with performing image enhancement by deconvolution. This simultaneous capability, based on a single acquisition of ultrasound data, has not been reported in previous publications. Our algorithm works by conducting non-blind deconvolution of the reflection data with point-spread functions based on different speeds of sound. Using a search strategy, we select the speed that produces the best-possible restoration. The deconvolution operates on the beamformed uncompressed radio-frequency data, without any need to modify the hardware of the ultrasound machine. A conventional handling of the transducer array is all that is required in the data acquisition part of our proposed method: the data can be collected freehand, unlike most other estimation methods. We have tested our algorithm with simulations, in vitro phantoms with known and unknown speeds and in vivo scans. The estimation error was found to be +0.19 +/- 8.90 m/s (mean +/- standard deviation) for in vitro in-house phantoms whose speeds were also measured independently. In addition to the speed estimation, our method has also proved to be capable of simultaneously producing a better restoration of ultrasound images than deconvolution by an assumed speed of 1540 m/s, when this assumption is incorrect.

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.

A regularized inverse approach to ultrasonic pulse-echo imaging

An inverse-theoretic approach to ultrasonic pulse-echo imaging based on nonquadratic regularization is presented, and its effectiveness is investigated computationally by: 1) evaluating the quality of the reconstruction of speckle-based images as a function of the transmit-receive bandwidth and focal number of the transducer; 2) comparing the reconstructed images with those obtained by using conventional B-mode imaging. The L-curve and the generalized cross-validation methods were evaluated as automatic regularization parameter selection techniques. The inversion using regularization produced better results than conventional B-mode imaging for high signal-to-noise ratios (SNRs). A lower bound of 30 dB for the SNR was found for this study, below which several of the image features were lost during the reconstruction process in order to control the distortion due to the noise.

Novel genetic-neuro-fuzzy filter for speckle reduction from sonography images

Edge-preserving speckle noise reduction is essential to computer-aided ultrasound image processing and understanding. A new class of genetic-neuro-fuzzy filter is proposed to optimize the trade-off between speckle noise removal and edge preservation. The proposed approach combines the advantages of the fuzzy, neural, and genetic paradigms. Neuro-fuzzy approaches are very promising for nonlinear filtering of noisy images. Fuzzy reasoning embedded into the network structure aims at reducing errors while fine details are being processed. The learning method based on the real-time genetic algorithms (GAs) performs an effective training of the network from a collection of training data and yields satisfactory results after a few generations. The performance of the proposed filter has been compared with that of the commonly used median and Wiener filters in reducing speckle noises on ultrasound images. We evaluate this filter by passing the filter's output to the edge detection algorithm and observing its ability to detect edge pixels.Experimental results show that the proposed genetic-neuro-fuzzy technique is very effective in speckle noise reduction as well as detail preserving even in the presence of highly noise corrupted data, and it works significantly better than other well-known conventional methods in the literature.

Robust deconvolution of high-frequency ultrasound images using higher-order spectral analysis and wavelets

Deconvolution of high-frequency (30-40 MHz) ultrasonic images of human skin was studied in vivo. Separate one-dimensional (1-D) functions for the axial and lateral profiles were first estimated using higher-order spectral methods. Subsequently, deconvolution was implemented us ing a regularized inverse Wiener filtering of the wavelet and scaling coefficients that were obtained after a wavelet decomposition of the RF signals. Deconvolution was first performed in the axial direction, then in the lateral direction. The methods were applied to data obtained from the skin of 16 volunteers using three different transducers. Significant improvements in both the axial and lateral resolutions were obtained in all the cases. Features such as hair follicles in the dermis and fingerprints on the surface of the finger were more clearly displayed in the processed images compared to the original images. The results indicate that the deconvolution method using higher-order spectral methods and wavelet analysis could significantly improve the quality of high-frequency ultrasonic skin images.

Robust estimation of ultrasound pulses using outlier-resistant de-noising

A different approach to the problem of estimation of the ultrasound pulse spectrum, which usually arises as a part of ultrasound image restoration algorithms, is presented. It is shown that this estimation problem can be reformulated in terms of a de-noising problem. In this formulation, the log-spectrum of a radio-frequency line (RF-line) is viewed as a noisy measurement of the signal that needs to be estimated, i.e., the ultrasound pulse log-spectrum. The log-spectrum of the tissue reflectivity function (i.e., tissue response) is considered as the noise to be rejected. The contribution of the paper is twofold. First, it provides statistical description of the reflectivity function log-spectrum for the case, when the samples of the reflectivity function are independent identically distributed (i.i.d.) Gaussian random variables. Moreover, it is shown that the problem of the pulse spectrum recovery is essentially a de-noising problem. Consequently, it is suggested to solve the problem within the framework of the de-noising by wavelet shrinkage. Second, a computationally efficient algorithm is proposed for the pulse-spectrum estimation, which can be viewed as a modified version of the classical Donoho's three-step de-noising procedure. This modification is necessary, because of specific properties of the noise to be rejected. It is shown, that whenever the samples of the reflectivity function can be assumed to be i.i.d. Gaussian random variables, the samples of its log-spectrum obey the Fisher-Tippet distribution. For this type of noise, straightforward implementation of the standard de-noising can cause serious estimation errors. In order to overcome this difficulty, an outlier-resistant de-noising is performed. The unique properties of this modified de-noising algorithm allow estimating the pulse spectrum adaptively to its properties, as they are continuously influenced by the frequency-dependent attenuation process. The performance of the proposed algorithm is examined in a series of computer-simulations. It is shown that this algorithm, developed on the assumption of the "Gaussian" reflectivity function, remains applicable for broader classes of distributions. The results obtained in a series of in vivo experiments reveal superior performance of the novel approach over some of alternative estimation techniques, e.g., cepstrum-based estimation.

Shift-invariant, DWT-based "projection" method for estimation of ultrasound pulse power spectrum

An approach to computing estimates of the ultrasound pulse spectrum from echo-ultrasound RF sequences, measured from biological tissues, is proposed. It is computed by a "projection" algorithm based on the Discrete Wavelet Transform (DWT) using averaging over a range of linear shifts. It is shown that the robust, shift invariant estimate of the ultrasound pulse power spectrum can be obtained by the projection of RF line log spectrum on an appropriately chosen subspace of L2(R) (i.e., the space of square-integrable functions) that is spanned by a redundant collection of compactly supported, scaling functions. This redundant set is formed from the traditional (in Wavelet analysis) orthogonal set of scaling functions and also by all its linear (discrete) shifts. A proof is given that the estimate, so obtained, could be viewed as the average of the orthogonal projections of the RF line log spectrum, computed for all significant linear shifts of the RF line log spectrum in frequency domain. It implies that the estimate is shift-invariant. A computationally efficient scheme is presented for calculating the estimate. Proof is given that the averaged, shift-invariant estimate can be obtained simply by a convolution with a kernel, which can be viewed as the discretized auto-correlation function of the scaling function, appropriate to the particular subspace being considered. It implies that the computational burden is at most O(n log2 n), where n is the problem size, making the estimate quite suitable for real-time processing. Because of the property of the wavelet transform to suppress polynomials of orders lower than the number of the vanishing moments of the wavelet used, the presented approach can be considered as a local polynomial fitting. This locality plays a crucial role in the performance of the algorithm, improving the robustness of the estimation. Moreover, it is shown that the "averaging" nature of the proposed estimation allows using (relatively) poorly regular wavelets (i.e., short filters), without affecting the estimation quality. The latter is of importance whenever the number of calculations is crucial.

Aberration correction for time-domain ultrasound diffraction tomography

Extensions of a time-domain diffraction tomography method, which reconstructs spatially dependent sound speed variations from far-field time-domain acoustic scattering measurements, are presented and analyzed. The resulting reconstructions are quantitative images with applications including ultrasonic mammography, and can also be considered candidate solutions to the time-domain inverse scattering problem. Here, the linearized time-domain inverse scattering problem is shown to have no general solution for finite signal bandwidth. However, an approximate solution to the linearized problem is constructed using a simple delay-and-sum method analogous to "gold standard" ultrasonic beamforming. The form of this solution suggests that the full nonlinear inverse scattering problem can be approximated by applying appropriate angle- and space-dependent time shifts to the time-domain scattering data; this analogy leads to a general approach to aberration correction. Two related methods for aberration correction are presented: one in which delays are computed from estimates of the medium using an efficient straight-ray approximation, and one in which delays are applied directly to a time-dependent linearized reconstruction. Numerical results indicate that these correction methods achieve substantial quality improvements for imaging of large scatterers. The parametric range of applicability for the time-domain diffraction tomography method is increased by about a factor of 2 by aberration correction.

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, although a more detailed description can be found in our companion paper [1]. 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.