Mohammad Reza Hajihashemi

Shape Reconstruction Using the Level Set Method for Microwave Applications

A shape reconstruction algorithm based on contour deformation using the full-band level set method is presented. Transverse magnetic plane waves are used for excitation. The results of full-band level set scheme are compared with those of narrowband scheme. A proposed measurement configuration is shown to produce more accurate results.

TE Versus TM for the Shape Reconstruction of 2-D PEC Targets Using the Level-Set Algorithm

The transverse electric (TE) polarization for shape reconstruction of perfect electric conducting 2-D targets is presented. The deformation velocity for the TE polarization case is implemented in the level-set algorithm. A comparison between the reconstruction CPU time between the TE and transverse magnetic (TM) polarizations is discussed. The numerical results show that retrieving the shape and location of multiple targets of arbitrary cross sections becomes computationally intensive when illumination with TE-polarized waves is used. If the orientation of the unknown cylinders is a priori known, the TM-polarized waves provide faster reconstruction results with the same accuracy compared with the TE-polarized waves. Upon corrupting the synthetic data with Gaussian noise up to signal-to-noise ratio of 5 dB, the TM polarization seems to provide more accurate results compared with the TE case.

Experimental Microwave Validation of Level Set Reconstruction Algorithm

The capability of the level set method is illustrated for shape and location reconstruction using real measurement data in the range of 3-8 GHz. An experimental setup is utilized to measure the S-parameters using two Vivaldi antennas revolving around metallic pipes of different cross-sections. A two-dimensional reconstruction of the pipes cross section is retrieved using the level set algorithm combined with the method of moments and the frequency hopping technique. The results show good agreement between the reconstructed cross section and the true configuration. This indicates to the strength of the level set method and its ability to cope with the noise in real measurements.

Level Set Algorithm for Shape Reconstruction of Non-Overlapping Three-Dimensional Penetrable Targets

This paper presents a 3-D shape reconstruction algorithm based on the level set method. Multiple dielectric and non-overlapping objects are considered. The level set algorithm is a gradient-type optimization approach that aims to minimize a cost function between measurements and computer-simulated data. The algorithm is capable of retrieving the shape and location of multiple targets made of two different and slightly lossy materials. An appropriate form of the deformation velocity based on the forward and adjoint fields is calculated. The method of moment surface integral equation is implemented to calculate the deformation velocity of the evolving objects. Two sets of Hamilton-Jacobi equations, associated with the two dielectric materials, are solved simultaneously to update the evolving objects. During the inversion scheme, the marching cubes method is employed to restore the surface meshes necessary for the forward solver. The algorithm is tested on corrupted synthetic data with signal-to-noise ratio of 10 dB.

INVERSE SCATTERING OF THREE-DIMENSIONAL PEC OBJECTS USING THE LEVEL-SET METHOD

A 3D shape reconstruction algorithm for multiple PEC objects immersed in air is presented. The Hamilton-Jacobi PDE is solved in the entire computational domain with employing the marching cubes method to retrieve the unknown objects. The method of moment surface integral equation is used as the forward solver. An appropriate form of the deformation velocity, based on the forward and adjoint flelds, is implemented to minimize the mismatch between the measurements and simulated scattered flelds from the evolving objects. The inversion algorithm demonstrated good shape reconstruction results even when using limited view data or noisy corrupted data with SNR of 5dB.

Drift Denoising of Experimental TE Measurements for Imaging 2D PEC Cylinders

This work presents shape reconstruction results using TE experimental scattering data of a perfect electric conducting (PEC) cylinder. The level set method combined with the method of moments is used for the reconstruction. The experimental data are collected using two ultrawideband strip-fed dielectric resonator antennas rotating around the target. The removal of the drift noise is achieved through spatial low-pass filtering, which is a key element to improve the reconstruction.

Noninvasive Evaluation of Nuclear Morphometry in Breast Lesions Using Multispectral Diffuse Optical Tomography

Breast cancer is the most prevalent cancer and the main cause of cancer-related death in women worldwide. There are limitations associated with the existing clinical tools for breast cancer detection and alternative modalities for early detection and classification of breast cancer are urgently needed. Here we describe an optical imaging technique, called multispectral diffuse optical tomography (DOT), and demonstrate its ability of non-invasively evaluating nuclear morphometry for differentiating benign from malignant lesions. Photon densities along the surface of the breast were measured to allow for the extraction of three statistical parameters including the size, elongation and density of nuclei inside the breast tissue. The results from 14 patients (4 malignant and 10 benign lesions) show that there exist significant contrasts between the diseased and surrounding normal nuclei and that the recovered nuclear morphological parameters agree well the pathological findings. We found that the nuclei of cancer cells were less-spherical compared with those of surrounding normal cells, while the nuclear density or volume fraction provided the highest contrast among the three statistical parameters recovered. This pilot study demonstrates the potential of multispectral DOT as a cellular imaging method for accurate determination of breast cancer.

High performance computing for the level-set reconstruction algorithm

A parallelized version of the level-set algorithm based on the MPI technique is presented. TM-polarized plane waves are used to illuminate two-dimensional perfect electric conducting targets. A variety of performance measures such as the efficiency, the load balance, the weak scaling, and the communication/computation times are discussed. For electromagnetic inverse scattering problems, retrieving the targets arbitrary shape and location in real time is considered as a main goal, even as a trade-off with algorithm efficiency. For the three cases considered here, a maximum speedup of 53X-84X is achieved when using 256 processors. However, the overall efficiency of the parallelized level-set algorithm is 21%-33% when using 256 processors and 26%-52% when using 128 processors. The effects of the bottlenecks of the level-set algorithm on the algorithm efficiency are discussed.

Morphologic tomography of nonspherical particles using multispectral diffusing light measurements.

A series of phantom experiments are conducted to demonstrate the ability of a T-matrix-based inverse algorithm for tomographic recovery of morphologic characteristics of nonspherical particles embedded in heterogeneous turbid media. Diffusely scattered light at several wavelengths along the boundary of the phantom are collected and analyzed to allow for simultaneous extraction of the size, concentration, and aspect ratio of the spheroidal particles.

Inverse Scattering Shape Reconstruction of 3D Bacteria Using the Level Set Algorithm

Bacteria exist in a variety of groups of shapes, sizes, and single or multiple cell formations. In this paper, the level set shape reconstruction technique, the method of moments, and the marching cubes methods are integrated in the high frequency band for imaging three dimensional bacteria. The time step and the resolution of the marching cubes method are investigated to smooth the error function of the level set and hence speed up the convergence at high frequencies. The numerical results demonstrate the robustness of the level set algorithm for the detection of bacteria based on their shapes. The three dimensional shape reconstructions of unknown bacteria can be utilized to classify biological warfare agents.