Regularized algorithms for applications in microwave thermometry
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2024
Författare
Alsaberi, Rani
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
This study explores the optimization of the regularization parameter for Tikhonov’s
functional, which is derived from the vector wave equation, a partial differential
equation (PDE), and transformed into a volume integral equation. Solving this
equation using Tikhonov’s functionals provides three different approaches, each with
varying numbers of regularization parameters. To identify the optimal regularization
parameters, three methods were employed: the L-curve method, the fixed point
algorithm, and Morozov’s discrepancy principle.
The L-curve method and the fixed point algorithm both indicated that a regularization
parameter of 1 is optimal, yielding acceptable results across various reconstruction
scenarios. However, Morozov’s discrepancy principle consistently produced
superior results, albeit with a significant dependency on the initial reconstruction
matrix. Ultimately, while Morozov’s discrepancy principle shows the most promise
for optimizing Tikhonov’s functional, it is not yet viable for practical use without
further refinement. Moreover, compared to previous studies with a similar setup,
this study employs the finite difference method, unlike past works where the finite
element method was employed.
The code can be found at the link given in [28].
Beskrivning
Ämne/nyckelord
Tikhonov’s functional, regularization parameter, L-curve method, fixed point algorithm, Morozov’s discrepancy principle, hyperthermia, ill-posed problem.