Nonperturbative diffraction tomography via Gauss-Newton iteration applied to the scattering integral equation.

A nonperturbational inverse scattering solution for the scattering integral equation (SIE) is presented. The numerical discretization of the SIE is performed by the moment method (MM) using sinc basis functions. Previous algorithms using the alternating variable (AV) nonlinear iteration with algebraic reconstruction technique (ART) solution of the linearizations are shown to diverge for high contrast/large size acoustic scatterers. This deficiency is alleviated by the use of the Gauss-Newton (GN) nonlinear iteration with conjugate gradient (CG) solution of the linearizations. Further numerical efficiency is attained by use of the biconjugate gradient (BCG) algorithm to solve the forward scattering problems. Test problem reconstructions of circular cylinders, using the Bessel series analytic solution to generate the scattering data, demonstrate the accuracy of the method. Inhomogeneous models of human cross-sections verify the high spatial resolution and high speed of sound contrast capability of the method.

A concave annular array design, based on phasor summation--Part I: Design methodology.

A detailed method for the design of annular arrays based on phasor summation is developed. The net phase shift across each annulus obtained by phasor summation is a very important factor in the design of an annular array, and determines the strength of the signal received. The method presented in this paper allows the designer to evaluate the trade-offs in parameters such as the strength of the signal from each annulus, the efficiency of each annulus, and the depth of focus that would be achievable. A concave annular array has been fabricated according to this design method. A set of graphs are given for an actual design to illustrate how one may readily evaluate these trade-offs.

A concave annular array design, based on phasor summation--Part II: Beam profiles and resultant images by B-scan and synthetic focus methods.

A brief review of the synthetic focusing method is given. The theoretical limit of resolution that may be achieved with the synthetic focusing methods is demonstrated using experimental results on a thin thread obtained with an annular array whose design was given in Part I. The advantage of large aperture arrays is illustrated by an in vitro reflection image of a dog artery, made with this array, that has at least four times the spatial resolution of present clinical B-scanners operating in the same frequency range.

Inverse scattering solutions by a sinc basis, multiple source, moment method--Part III: Fast algorithms.

olving the inverse scattering problem for the Helmholtz wave equation without employing the Born or Rytov approximations is a challenging problem, but some slow iterative methods have been proposed. One such method suggested by us is based on solving systems of nonlinear algebraic equations that are derived by applying the method of moments to a sinc basis function expansion of the fields and scattering potential. In the past, we have solved these equations for a 2-D object of n by n pixels in a time proportional to n5. In the present paper, we demonstrate a new method based on FFT convolution and the concept of backprojection which solves these equations in time proportional to n3 X log(n). Several numerical examples are given for images up to 7 by 7 pixels in size. Analogous algorithms to solve the Riccati wave equation in n3 X log(n) time are also suggested, but not verified. A method is suggested for interpolating measurements from one detector geometry to a new perturbed detector geometry whose measurement points fall on a FFT accessible, rectangular grid and thereby render many detector geometrics compatible for use by our fast methods.

Emission-computed tomography and its application to imaging of acute myocardial infarction in intact dogs using Tc-99m pyrophosphate.

The techniques of emission-computed tomography have been used to obtain in vivo quantitative estimates of the three-dimensional distribution of gamma-emitting radionuclides in dog hearts. Conjugate views, obtained for 60 equiangular projections around 360 degrees by rotating the object in front of a gamma camera, were used to reconstruct multiple-level emission transaxial images for various test objects, and for dogs with surgically induced acute myocardial infarcts. Corrections for attenuation were performed in the backprojection step of the convolution algorithm used for reconstruction. Quantitative estimates of the spatial extent and concentration of activity were obtained to within 10--15% rms error. Correlations were obtained between the radionuclide and histopathologic estimates of the extent and location of infarction.

Computed transaxial imaging using single gamma emitters.

Emission computed tomography (ECT) studies were performed on test objects and dogs. Conjugate views were obtained for 60 to 120 projections equispaced around 360 degrees by rotation of the subjects in front of a gamma camera. A convolution reconstruction algorithm in which gamma ray attenuation corrections are included in the backprojection step were used to reconstruct the emission images. Reconstructions of x-ray transmission data provided data for gamma ray attenuation corrections of the emission images of 99mTc-pyrophosphate uptake in dogs. Reconstructed images of test objects show spatial resolution uniformity, and attenuation corrections enable estimation of relative activity densities to within 10--15% rms errors, thus demonstrating quantitative imaging capabilities of emission CT.