A study on the reconstruction of moderate contrast targets using the distorted born iterative method

Abstract

Previous tomographic methods using ultrasound for reconstructing sound speed and attenuation images suffered from convergence issues for targets with moderate speed of sound contrast. Convergence problems can be overcome by the use of the multiple frequency, distorted Born iterative method (DBIM). The implementation of DBIM for measurement configurations in which receiver positions are fixed was studied, and a novel regularization scheme was developed. The regularization parameter needed to stabilize the inversion process initially was found through the Rayleigh quotient iteration, then relaxed according to the relative residual error between the measured and estimated scattered fields. The DBIM was successfully stabilized for both full and partial receiver angular coverage without a significant loss in spatial resolution. The effects of variable density in the reconstructions were briefly explored through simulations. The ability to reconstruct targets with moderate contrast was validated through experimental measurements. Speed of sound profiles for balloons filled with saline in a background of water were reconstructed using multiple frequency DBIM techniques. The mean squared error for speed of sound reconstructions of the balloon phantoms with 16.4% sound speed contrast was 1.1%.

Sound contrast imaging using uniform ring configuration of transducers with reconstruction

“…In [11] by using multiple transmitters and dete equal distances. This configuration would large, thus, it is not efficient for the itera In this paper, we propose to use a sampling configuration of detectors, with detectors is smaller than that in t configuration.…”

“…, (11) where is the ( vector, contains the difference between predicted and measured scattered ultrasound signals;…”

Fast inverse scattering solutions using the distorted Born iterative method and the multilevel fast multipole algorithm

“…In analogy with the frequency hopping employed to solve multiple-frequency imaging problems, 8,9,15,20,30,38,39 the round-robin technique attempts to avoid local minima associated with the solution of a single, restricted inverse problem ͑e.g., involving a single imaging frequency and a limited set of transmit angles͒ by using a previously obtained solution as a starting guess for a subsequent inversion. If local minima associated with distinct transmit angles do not coincide, a solution stagnating in a local minimum for one transmit angle may move away from the local minimum and toward the global minimum when the transmit angle is shifted.…”

“…The choice of regularization parameter ͑23͒ was motivated by spectral analysis of the Fréchet derivative operator for two-dimensional scattering geometries. 8 When the round-robin technique is employed, the importance of regularization is diminished. The underdetermined system of equations resulting from inversion of the Fréchet derivative operator of a limited number of transmit angles is inverted using the minimum-norm technique ͓Eq.…”

“…6 The method was originally applied to two-dimensional electromagnetic problems in free space, but has been implemented to solve acoustic problems [7][8][9][10] and electromagnetic problems in three dimensions. [11][12][13][14][15] A distinct but mathematically equivalent method has been applied to two-dimensional acoustic problems.…”