An Eigenfunction Method for Reconstruction of Large-Scale and High-Contrast Objects

Deep sub-wavelength focusing has been demonstrated for locally resonant metamaterials using electromagnetic and acoustic waves. The elastic equivalents of such objects are made of sub-wavelength resonating beams fixed to a two-dimensional plate, as presented here. Independent of a random or regular arrangement of the resonators, the metamaterial shows large bandgaps that are independent of the incident wave direction. Numerical simulations demonstrate that the insertion of a defect in the layout, as a shorter resonator, creates strong amplification of the wave-field on the defect. This energy trapping, which is localized on a spatial scale that is much smaller than the wavelength in the two-dimensional plate, leads to a >1 factor in terms of the local density of energy.

Section: Introductionmentioning

confidence: 99%

Sub-wavelength energy trapping of elastic waves in a metamaterial

Colombi

Roux

Rupin

2014

“…4, and the eigenfunction expansion methods detailed in Ref. [5][6][7]. One reason for continuing to pursue new approaches is the high cost in computation time involved in forming nonlinear solutions.…”

Section: Introductionmentioning

confidence: 99%

Born iterative reconstruction using perturbed-phase field estimates

Astheimer

Waag²

2008

A method of image reconstruction from scattering measurements for use in ultrasonic imaging is presented. The method employs distorted-wave Born iteration but does not require using a forward-problem solver or solving large systems of equations. These calculations are avoided by limiting intermediate estimates of medium variations to smooth functions in which the propagated fields can be approximated by phase perturbations derived from variations in a geometric path along rays. The reconstruction itself is formed by a modification of the filtered-backpropagation formula that includes correction terms to account for propagation through an estimated background. Numerical studies that validate the method for parameter ranges of interest in medical applications are presented. The efficiency of this method offers the possibility of real-time imaging from scattering measurements.

“…(14), iterative solution methods such as the generalized minimal residual method (GMRES) 26 or the stabilized biconjugate gradient method (BiCG-STAB) 27 are employed in concert with the FMM to solve Eq. (11) efficiently without the need to explicitly construct the Green's matrix (13). This pairing allows each iteration to be computed in O(N) time and with O(N) storage.…”

Section: A the Fast Multipole Methodsmentioning

confidence: 99%

“…[11][12][13] These techniques require repeated evaluation of forward scattering for determining successive updates to estimates of the medium. Improved methods that are applicable in clinical settings require realistic scattering data to provide realistic evaluations of performance.…”

Section: Introductionmentioning

confidence: 99%

Comparison of temporal and spectral scattering methods using acoustically large breast models derived from magnetic resonance images

Hesford

Tillett

Astheimer

et al. 2014

Accurate and efficient modeling of ultrasound propagation through realistic tissue models is important to many aspects of clinical ultrasound imaging. Simplified problems with known solutions are often used to study and validate numerical methods. Greater confidence in a timedomain k-space method and a frequency-domain fast multipole method is established in this paper by analyzing results for realistic models of the human breast. Models of breast tissue were produced by segmenting magnetic resonance images of ex vivo specimens into seven distinct tissue types. After confirming with histologic analysis by pathologists that the model structures mimicked in vivo breast, the tissue types were mapped to variations in sound speed and acoustic absorption. Calculations of acoustic scattering by the resulting model were performed on massively parallel supercomputer clusters using parallel implementations of the k-space method and the fast multipole method. The efficient use of these resources was confirmed by parallel efficiency and scalability studies using large-scale, realistic tissue models. Comparisons between the temporal and spectral results were performed in representative planes by Fourier transforming the temporal results. An RMS field error less than 3% throughout the model volume confirms the accuracy of the methods for modeling ultrasound propagation through human breast.