OGG-FDTD Method with B2-Spline Interpolation in FBTS for Arbitrary Shapes Reconstruction

Bong, Siaw-Wee (2020) OGG-FDTD Method with B2-Spline Interpolation in FBTS for Arbitrary Shapes Reconstruction. PhD thesis, Universiti Malaysia Sarawak (UNIMAS).

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Abstract

Microwave tomography is the new technology which evaluates buried or embedded objects in a medium by using Electromagnetic (EM) waves. Finite-Difference Time-Domain (FDTD) method is a simple and powerful tool used to solve EM problems. It can investigate multiple frequencies without any extra computational effort. However, the main drawback of the FDTD method is difficult to exactly generate meshes for electromagnetic structures with curved boundaries and small features due to its restriction to inherent orthogonal grids. To address this issue, the B2-spline or biquadratic spline interpolation technique for Overset Grid Generation and Finite-Difference Time-Domain (OGG-FDTD) method was proposed as a new numerical method to overcome the limitation of FDTD method. The OGG-FDTD method consists of two meshes that are main-mesh and sub-mesh. The main-mesh is also known as FDTD lattice which is covers the entire computational domain. The sub-mesh is known as minor grid which it is placed on top of the main mesh to form a single mesh. The overlapping region between the main mesh and sub-mesh can be obtained by using the B2-spline interpolation technique. The proposed numerical method has the ability to accurately measure the EM scattered field for an unknown object in a different medium. The results showed that the OGG-FDTD method with B2-spline interpolation gave lower relative error than bilinear interpolation with 0.0009% of difference in free space, 0.0033% of difference in Case A dielectric medium, 0.236% of difference in Case B dielectric medium, and 0.003% of difference in Case C dielectric medium. The OGG-FDTD method with B2-spline interpolation was extended by incorporating the Forward-Backward Time Stepping (FBTS) technique for arbitrary shaped objects detection and reconstruction. The performance of the proposed method was evaluated by investigating the characteristics of the buried objects in transverse magnetic z-plane (TMz) mode. Different type of buried objects including square, circular, triangular and arbitrary shapes were used to validate the competency of the proposed method. The results showed that the Mean Square Error (MSE) of reconstructed dielectric profiles by using the proposed method has achieved significantly lower values than the FDTD method in FBTS. In Case I, the accuracy difference between the two methods was 26.67% for relative permittivity and 27.63% for conductivity, respectively. Further, the efficacy of this proposed method is applied to homogeneous and inhomogeneous breast cancer detection applications. In order to demonstrate the validity of this proposed method, the mostly fatty and extremely dense homogeneous breasts were chosen in this research. Then, the heterogeneous realistic breast phantom from Nagasaki University Hospital was chosen for inhomogeneous breast cancer detection application as Case M. The results showed that the implementation of the proposed method increased the accuracy of reconstructed the relative permittivity image by 50.54%, and conductivity by 74.42% as compared to the FDTD method in FBTS technique. Hence, it is proven that this numerical method can provide clearer and better reconstructed images to improve the quality of retrieve the dielectric profiles of the investigation area.

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