Qing Huo Liu

The PSTD algorithm: A time-domain method requiring only two cells per wavelength

A pseudospectral time-domain (PSTD) method is developed for solutions of Maxwells equations. It uses the fast Fourier transform (FFT), instead of finite differences on conventional finite-difference–time-domain (FDTD) methods, to represent spatial derivatives. Because the Fourier transform has an infinite order of accuracy, only two cells per wavelength are required, compared to 8–16 cells per wavelength required by the FDTD method for the same accuracy. The wraparound effect, a major limitation caused by the periodicity assumed in the FFT, is removed by using Berengers perfectly matched layers. The PSTD method is a factor of 4D–8D more efficient than the FDTD methods (D is the dimensionality).

PERFECTLY MATCHED LAYERS FOR ELASTODYNAMICS: A NEW ABSORBING BOUNDARY CONDITION

The use of perfectly matched layers (PML) has recently been introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, we will first prove that a fictitious elastodynamic material half-space exists that will absorb an incident wave for all angles and all frequencies. Moreover, the wave is attenuative in the second half-space. As a consequence, layers of such material could be designed at the edge of a computer simulation region to absorb outgoing waves. Since this is a material ABC, only one set of computer codes is needed to simulate an open region. Hence, it is easy to parallelize such codes on multiprocessor computers. For instance, it is easy to program massively parallel computers on the SIMD (single instruction multiple data) mode for such codes. We will show two- and three-dimensional computer simulations of the PML for the linearized equations of elastodynamics. Comparison with Liao’s ABC will be given.

Through-wall imaging (TWI) by radar: 2-D tomographic results and analyses

A two-dimensional nonlinear inverse scattering technique is developed for imaging objects in a multilayered medium that simulates the effects of building walls in the context of through-wall imaging (TWI). The effectiveness and capacity of the inversion algorithm and the feasibility of through-wall imaging is demonstrated via a number of numerical examples. It has been shown that using multifrequency data high-quality image reconstruction can be achieved with a limited array view.

An accurate algorithm for nonuniform fast Fourier transforms (NUFFT's)

Based on the (m, N, q)-regular Fourier matrix, a new algorithm is proposed for fast Fourier transform (FFT) of nonuniform (unequally spaced) data. Numerical results show that the accuracy of this algorithm is much better than previously reported results with the same computation complexity of O(N log/sub 2/ N). Numerical examples are shown for the applications in computational electromagnetics.

Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-CT

Recent advances in murine cardiac studies with three-dimensional (3D) cone beam micro-CT used a retrospective gating technique. However, this sampling technique results in a limited number of projections with an irregular angular distribution due to the temporal resolution requirements and radiation dose restrictions. Both angular irregularity and undersampling complicate the reconstruction process, since they cause significant streaking artifacts. This work provides an iterative reconstruction solution to address this particular challenge. A sparseness prior regularized weighted l2 norm optimization is proposed to mitigate streaking artifacts based on the fact that most medical images are compressible. Total variation is implemented in this work as the regularizer for its simplicity. Comparison studies are conducted on a 3D cardiac mouse phantom generated with experimental data. After optimization, the method is applied to in vivo cardiac micro-CT data.

The perfectly matched layer for acoustic waves in absorptive media

The perfectly matched layer (PML) was first introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. It was first proven by Chew and Liu that a fictitious elastic PML half-space also exists in solids, which completely absorbs elastic waves, in spite of the coupling between compressional and shear waves. The PML absorbing boundary condition provides much higher absorption than other previous ABCs in finite-difference methods. In this work, a method is presented to extend the perfectly matched layer to simulating acoustic wave propagation in absorptive media. This nonphysical material is used at the computational edge of a finite-difference time-domain (FDTD) algorithm as an ABC to truncate unbounded media. Two aspects of the acoustic PML are distinct: (a) For a perfectly matched layer in an intrinsically absorptive medium, an additional term involving the time-integrated pressure field has to be introduced to account for the coupling between the loss from the PML a...

Three-dimensional nonlinear image reconstruction for microwave biomedical imaging

Active microwave imaging has attracted significant interests in biomedical applications, in particular for breast imaging. However, the high electrical contrasts in breast tissue also increases the difficulty of forming an accurate image because of the increased multiple scattering. To model such strong three-dimensional (3-D) multiple scattering effects in biomedical imaging applications, we develop a full 3-D inverse scattering algorithm based on the combination of the contrast source inversion and the fast Fourier transform algorithm. Numerical results show that our algorithm can accurately invert for the high-contrast media in breast tissue.

The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media

The perfectly matched layer (PML) was first introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, a method is developed to extend the perfectly matched layer to simulating seismic wave propagation in poroelastic media. This nonphysical material is used at the computational edge of a finite-difference algorithm as an ABC to truncate unbounded media. The incorporation of PML in Biots equations is different from other PML applications in that an additional term involving convolution between displacement and a loss coefficient in the PML region is required. Numerical results show that the PML ABC attenuates the outgoing waves effectively.

Active microwave imaging. I. 2-D forward and inverse scattering methods

Active microwave imaging (MWI) for the detection of breast tumors is an emerging technique to complement existing X-ray mammography. The potential advantages of MWI arise mainly from the high contrast of electrical properties between tumors and normal breast tissue. However, this high contrast also increases the difficulty of forming an accurate image because of increased multiple scattering. To address this issue, we develop fast forward methods based on the combination of the extended Born approximation, conjugate- and biconjugate-gradient methods, and the fast Fourier transform. We propose two nonlinear MWI algorithms to improve the resolution for the high-contrast media encountered in microwave breast-tumor detection. Numerical results show that our algorithms can accurately model and invert for the high-contrast media in breast tissue. The outcome of the inversion algorithms is a high-resolution digital image containing the physical properties of the tissue and potential tumors.

Electromagnetic time-reversal imaging of a target in a cluttered environment

Electromagnetic time-reversal imaging is addressed for a target situated in a cluttered background. We first investigate the theory of electromagnetic time-reversal imaging, followed by an experimental demonstration. A transmitter-receiver antenna array is connected to a network analyzer and applied to transmit wideband waveforms for detecting a target within a cluttered environment. We assume the cluttered background is fixed, thus the target signature is extracted by observing changes manifested by the introduction of a target. A numerical algorithm is required for computation of the Greens function employed within the time-reversal imager, with this implemented here via ray tracing. Example time-reversal images of different cluttered backgrounds and different targets are presented using measured data, with comparisons to a traditional radar imaging technique. Results show that the time-reversal imagery yields good focusing at the target, significantly better than when the background is not accounted for.