Pawan Chaturvedi

2-D companding for noise reduction in strain imaging

Companding is a signal preprocessing technique for improving the precision of correlation-based time delay measurements. In strain imaging, companding is applied to warp 2-D or 3-D ultrasonic echo fields to improve coherence between data acquired before and after compression. It minimizes decorrelation errors, which are the dominant source of strain image noise. The word refers to a spatially variable signal scaling that compresses and expands waveforms acquired in an ultrasonic scan plane or volume. Temporal stretching by the applied strain is a single-scale (global), 1-D companding process that has been used successfully to reduce strain noise. This paper describes a two-scale (global and local), 2-D companding technique that is based on a sum-absolute-difference (SAD) algorithm for blood velocity estimation. Several experiments are presented that demonstrate improvements in target visibility for strain imaging. The results show that, if tissue motion can be confined to the scan plane of a linear array transducer, displacement variance can be reduced two orders of magnitude using 2-D local companding relative to temporal stretching.

Testing the limitations of 2-D companding for strain imaging using phantoms

Companding may be used as a technique for generating low-noise strain images. It involves warping radio-frequency echo fields in two dimensions and at several spatial scales to minimize decorrelation errors in correlation-based displacement estimates. For the appropriate experimental conditions, companding increases the sensitivity and dynamic range of strain images without degrading contrast or spatial resolution significantly. In this paper, we examine the conditions that limit the effectiveness of 2-D local companding through a series of experiments using phantoms with tissue-like acoustic and elasticity properties. We found that strain noise remained relatively unchanged as the applied compression increased to 5% of the phantom height, while target contrast increased in proportion to the compression. Controlling the image noise at high compressions improves target visibility over the broad range induced in elastically heterogeneous media, such as biological tissues. Compressions greater than 5% introduce large strains and complex motions that reduce the effectiveness of companding. Control of boundary conditions and ultrasonic data sampling rates is critical for a successful implementation of our algorithms.

Electromagnetic imaging of underground targets using constrained optimization

Several high-frequency electromagnetic techniques have been used in recent years to detect and identify buried objects. Post-processing of the collected data is performed in many of these techniques to obtain high-quality images of buried targets. Accurate reconstructions of the targets constitutive parameters can be obtained by casting the imaging problem in terms of an inverse electromagnetic scattering problem. A number of techniques have been put forth recently to invert the electromagnetic data to obtain such images. The authors use a frequency-domain Born iterative method to reconstruct images of shallow targets. The Born iterative technique requires successive solutions to a forward scattering problem followed by an inverse scattering problem at each iteration step. They use a finite-difference time-domain (FDTD) algorithm to solve the forward scattering problem and constrained optimization for the inverse problem. Two-dimensional simulated data for several canonical objects buried in the ground are obtained using the FDTD technique. The same FDTD code is also used in calculating the Greens function required for solving the constrained optimization problem. Lossy, inhomogeneous ground models are used in several simulations to illustrate the use of this technique for practical situations. The inversion process can be used to reconstruct images for many realistic dielectric contrasts for which a linear Born approximation fails. Moreover, it is also shown that a small number of measurements results in accurate reconstructions with this technique. Use of multiple frequencies is also investigated. >

Error bounds on ultrasonic scatterer size estimates

Precision errors that occur in estimating the average scatterer size from pulse-echo ultrasound waveforms are examined in detail. The method-independent lower bound on estimation error is found from the Cramér-Rao inequality for comparison with the predicted error for the measurement technique currently used to estimate scatterer sizes in soft biological tissues. The probability density function for the estimate is also derived. From these statistical analyses, strategies for designing experiments that minimize the error are discussed. It is shown that compared with biological variability, measurement errors in scatterer size estimates are relatively large. Consequently, there is reason to continue searching for more efficient estimators. Although the analysis and results are derived for Gaussian correlation models that have been used to study the function and structure of kidneys, generalization to include correlation models for other tissues is straightforward.

Maximum-likelihood approach to strain imaging using ultrasound

A maximum-likelihood (ML) strategy for strain estimation is presented as a framework for designing and evaluating bioelasticity imaging systems. Concepts from continuum mechanics, signal analysis, and acoustic scattering are combined to develop a mathematical model of the ultrasonic waveforms used to form strain images. The model includes three-dimensional (3-D) object motion described by affine transformations, Rayleigh scattering from random media, and 3-D system response functions. The likelihood function for these waveforms is derived to express the Fisher information matrix and variance bounds for displacement and strain estimation. The ML estimator is a generalized cross correlator for pre- and post-compression echo waveforms that is realized by waveform warping and filtering prior to cross correlation and peak detection. Experiments involving soft tissuelike media show the ML estimator approaches the Cramer-Rao error bound for small scaling deformations: at 5 MHz and 1.2% compression, the predicted lower bound for displacement errors is 4.4 microns and the measured standard deviation is 5.7 microns.

Strain imaging with a deformable mesh

Ultrasonic strain imaging has drawn much attention recently because of its ability to noninvasively provide information on spatial variation of the elastic properties of soft tissues. Traditionally, local strain is estimated by scaling and cross correlating pre-and postcompression ultrasound echo fields. However, when the motion field generated by compression is more complex, scaling and cross correlation can no longer provide precise displacement estimates because of signal decorrelation. We introduce a new algorithm based on the deformable mesh method. This algorithm can accommodate more general forms of motion, namely, the motion that can be described by bilinear transformations. We applied the new algorithm to three sets of data in order to evaluate its performance. In the first set of data, primitive motions such as shearing and rotation are simulated. The second set of data is collected by compressing a tissue-mimicking phantom with three hard inclusions. The third experiment involves an ex vivo pig kidney embedded in a block of gelatin. The results from all three experiments show improvements with the new algorithm over other methods.

Ultrasonic and elasticity imaging to model disease-induced changes in soft-tissue structure

Ultrasonic techniques are presented for the study of soft biological tissue structure and function. Changes in echo waveforms caused by microscopic variations in the mechanical properties of tissue can reveal disease mechanism, in vivo. On a larger scale, elasticity imaging describes the macroscopic mechanical properties of soft tissues. We summarize the approach and present preliminary results for studying disease-induced changes in renal tissue using these two acoustic imaging techniques.

3-D companding using linear arrays for improved strain imaging

Three-dimensional (3-D) companding is applied to volume sets of RF echo signals to reduce decorrelation noise in strain images. Companding conditions echo signals to be cross-correlated to improve coherence and minimize decorrelation noise caused by complex 3-D motion. Previously, the authors showed that 2-D companding was able to eliminate decorrelation noise in strain images up to 50% compression if the out-of-plane displacement was negligible. This paper extends those methods to three dimensions, thus reducing the need to control boundary conditions. 3-D companding is also limited at high compressions (>5%) because of high strain gradients and rotation and shearing motions. A series of phantom studies illustrate the advantages and limitation of 3-D companding with and without aberrating layers.

Phantoms for elastography

Several viscoelastic properties of gelatin materials used in sonography and elastography phantoms are reported. Also reported is a device that was designed and built to make these measurements. Measurement precision with this device is typically within 1%. Finite element analysis was used to study boundary conditions and compressor size (compared to sample size) effects on the estimated elastic modulus. Results of these measurements indicate that gelatin gels are a good choice for elastography phantoms, but that the stiffness of these materials increases with time.

Signal processing strategies in acoustic elastography

Elastography is a remote sensing technique for imaging the elastic properties of biological tissues. An essential feature is tissue deformation (strain) that is measured by cross correlating ultrasonic echo waveforms acquired before and after a weak static compression. To fully exploit the large object contrast available among body tissues, many dependent experimental parameters must be carefully adjusted. This paper outlines a strategy for selecting the applied stress field including boundary conditions, transducer frequency and bandwidth, and echo window length and overlap that minimize elastographic noise and maximize dynamic range for a given spatial resolution.