Andrew E. Yagle

Lateral displacement estimation using tissue incompressibility

Using the incompressibility property of soft tissue, lateral displacements can be reconstructed from axial strain measurements. Results of simulations and experiments on gelatin-based tissue equivalent phantoms are compared with theoretical displacements, as well as estimates derived from traditional speckle tracking. Incompressibility processing greatly improves the accuracy and signal-to-noise ratio (SNR) of lateral displacement measurements compared with more traditional speckle tracking.

Fast algorithms for complex matrix multiplication using surrogates

Novel fast algorithms for multiplying square complex matrices are presented. The algorithms are based on concepts from fast methods of complex multiplication in which a surrogate is used for the square root of minus one. Previous methods imposed the structure of a finite ring or field on the problem. The novel algorithms also use a surrogate, but do not require the imposed structure and its inherent rounding. The number of real matrix multiplications required can be reduced from four to two for even dimension, and to 2+1/N/sup 2/ for odd dimension N. The disadvantage of the algorithms is the imposition of a requirement on the structure of one of the two complex matrices being multiplied. The 2*2 case of the algorithm can be adapted to computing Givens rotations, resulting in a 17% savings in real matrix multiplications. >

Forward and inverse problems in elasticity imaging of soft tissues

In elasticity imaging, a surface deformation is applied to an object using small pistons, and the resulting induced strains in the interior of the object are measured using ultrasonic imaging. Two important problems are considered: (1) the forward problem of determining the strains induced by a known deformation of an object with known elasticity; and (2) the inverse problem of reconstructing elasticity from measured strains and the equations of equilibrium. The method of finite differences is used to solve the forward problem for a given piston configuration; some nontrivial issues arise in determining boundary conditions. The finite difference equations are then rearranged into a linear system of equations which formulates the inverse problem; this system can be solved for the unknown elasticities. This formulation of the inverse problem is completely consistent with the forward problem; this is useful for iterative methods in which the deformation is adaptively changed. A comparison between simulated and actual measured results demonstrate the feasibility of the proposed procedure. >

A comparative analysis of several transformations for enhancement and segmentation of magnetic resonance image scene sequences

The performance of the eigenimage filter is compared with those of several other filters as applied to magnetic resonance image (MRI) scene sequences for image enhancement and segmentation. Comparisons are made with principal component analysis, matched, modified-matched, maximum contrast, target point, ratio, log-ratio, and angle image filters. Signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), segmentation of a desired feature (SDF), and correction for partial volume averaging effects (CPV) are used as performance measures. For comparison, analytical expressions for SNRs and CNRs of filtered images are derived, and CPV by a linear filter is studied. Properties of filters are illustrated through their applications to simulated and acquired MRI sequences of a phantom study and a clinical case; advantages and weaknesses are discussed. The conclusion is that the eigenimage filter is the optimal linear filter that achieves SDF and CPV simultaneously.

Optimal transformation for correcting partial volume averaging effects in magnetic resonance imaging

Segmentation of a feature of interest while correcting for partial volume averaging effects is a major tool for identification of hidden abnormalities, fast and accurate volume calculation, and three-dimensional visualization in the field of magnetic resonance imaging (MRI). The authors discuss the optimal transformation for simultaneous segmentation of a desired feature and correction of partial volume averaging effects while maximizing the signal-to-noise ratio (SNR) of the desired feature. It is proved that correction of partial volume averaging effects requires the removal of the interfering features from the scene. It is also proved that correction of partial volume averaging effects can be achieved merely by a linear transformation. It is shown that the optimal transformation matrix is easily obtained using the Gram-Schmidt orthogonalization procedure which is numerically stable. Applications of the technique to MRI simulation, phantom, and brain images are shown. It is shown that in all cases the desired feature is segmented from the interfering features and partial volume information is visualized in the resulting transformed images. >

The Schur Algorithm and its Applications

The Schur algorithm and its time-domain counterpart, the fast Cholseky recursions, are some efficient signal processing algorithms which are well adapted to the study of inverse scattering problems. These algorithms use a layer stripping approach to reconstruct a lossless scattering medium described by symmetric two-component wave equations which model the interaction of right and left propagating waves. In this paper, the Schur and fast Chokesky recursions are presented and are used to study several inverse problems such as the reconstruction of nonuniform lossless transmission lines, the inverse problem for a layered acoustic medium, and the linear least-squares estimation of stationary stochastic processes. The inverse scattering problem for asymmetric two-component wave equations corresponding to lossy media is also examined and solved by using two coupled sets of Schur recursions. This procedure is then applied to the inverse problem for lossy transmission lines.

Image reconstruction from projections under wavelet constraints

First, the authors discuss how the wavelet transform can be used to perform spatially-varying filtering of an image, suppressing noise locally in smooth regions of the image, and discuss detection of such regions in a noise-corrupted image. Second, they show how to compute the minimum mean-square estimate of an image given: (1) noisy projections of the image; (2) statistics of additive noise in the projections; and (3) constraints on wavelet coefficients of the image. Examples illustrate the resulting procedure. >

Application of the Schur algorithm to the inverse problem for a layered acoustic medium

The Schur algorithm is a signal processing algorithm which works on a layer‐stripping principle. Its time‐domain version, the fast Cholesky recursion, is a fast and efficient algorithm well‐suited for high‐speed data processing. In this paper, these algorithms are applied to the inverse problem for a continuous layered acoustic medium. Three different excitations of the medium are considered: impulsive plane waves at normal incidence, impulsive plane waves at oblique incidence, and spherical waves emanating from an impulsive point source. The fast algorithms obtained for each of these problems seem to be computationally superior to past work done on these problems that employed Gelfand–Levitan theory to reconstruct the potential of a Schrodinger equation.

Layer‐stripping solutions of multidimensional inverse scattering problems

A layer‐stripping procedure for solving three‐dimensional Schrodinger equation inverse scattering problems is developed. This method operates by recursively reconstructing the potential from the jump in the scattered field at the wave front, and then using the reconstructed potential to propagate the wave front and the scattered field further into the inhomogeneous region. It is thus a generalization of algorithms that have been developed for one‐dimensional inverse scattering problems. Although the procedure has not yet been numerically tested, the corresponding one‐dimensional algorithms have performed well on synthetic data. The procedure is applied to a two‐dimensional inverse seismic problem. Connections between simplifications of this method and Born approximation inverse scattering methods are also noted.

A layer‐stripping solution of the inverse problem for a one‐dimensional elastic medium

A fast algorithm for recovering profiles of density and Lame parameters as functions of depth for the inverse seismic problem in an elastic medium is obtained. The medium is probed with planar impulsive P- and SV-waves at oblique incidence, and the medium velocity components are measured at the surface. The interconversion of P- and SV-waves defines reflection coefficients from which the medium parameter profiles are obtained recursively. The algorithm works on a layer‐stripping principle, and it is specified in both differential and recursive forms. A physical interpretation of this procedure is given in terms of a lattice filter, where the first reflections of the downgoing waves in each layer yield the various reflection coefficients for that layer. A computer run of the algorithm on the synthetic impulsive plane‐wave responses of a twenty‐layer medium shows that the algorithm works satisfactorily.