A Discrete Dipole Approximation Forward Solver for Microwave Breast Imaging

Licentiate thesis, 2019

Breast cancer has the highest incidence rate of cancers in women worldwide. Early detection results in a higher survival rate. Drawbacks in conventional imaging modalities, including painful exams, have limited periodic breast screening. Microwave to mography has the potential to be a compelling alternative or complement to other imaging techniques. Advantages of microwave tomography is that it is harmless, comfortable, and cost effective. Microwave tomography has not yet fully been translated into the clinic, even if clinical trials are ongoing. 
One important challenge is high computational demands of microwave tomography algorithms. 3D tomography algorithms require multiple hours and a large amount of hardware resources to produce images. 3D imaging algorithms are usually implemented and tested for simulations setup and barely used in clinical settings. 2D microwave tomography algorithms are computationally less expensive compared to 3D algorithms. Few imaging groups have been successful in integrating the acquired 3D data into the 2D tomography algorithms for clinical applications. 
The microwave tomography algorithms include two main computation problems; forward and inverse. The forward problem has to be solved multiple times and the resulting computational cost is the time limiting step in microwave tomography algorithms, and this thesis is devoted to addressing it. 
In this thesis, the two-dimensional forward problem is modelled and formulated. In particular, the two-dimensional discrete dipole approximation (DDA) is proposed as a new forward solver for microwave tomography. The accuracy of the 2D DDA with respect to sampling number, size, and contrast of target are investigated. Moreover, the 2D DDA time efficiency and computation time are studied.
The forward solver computation times for direct, iterative, and iterative combined with fast Fourier transformation (FFT) solvers are calculated. The observations imply that the 2D DDA is an accurate, reliable, and rapid forward solver, and using the Krylov subspace methods combined with the FFT accelerate the computation time significantly.