Iterative fitting approach to CR-MREPT ; KR-MREÖT için yinelemeli yaklaştırma yöntemi

Cataloged from PDF version of article. ; Includes bibliographical references (leaves 67-70). ; Electrical properties (conductivity, and permittivity, ) imaging, reveals information about the contrast between tissues. Magnetic Resonance Electrical Properties Tomography (MREPT) is one of the electrical properties imaging techniques, which provides conductivity and permittivity images at Larmor frequency using the perturbations in the transmit magnetic eld, B+ 1 . Standard-MREPT (std-MREPT) method is the simplest method for obtaining electrical properties from the B+ 1 eld distribution, however it su ers from the boundary artifacts between tissue transitions. In order to eliminate this artifact, many methods are proposed. One such method is the Convection Reaction equation based MREPT (cr-MREPT). cr-MREPT method solves the boundary artifact problem, however Low Convective Field (LCF) artifact occurs in the resulting electrical property images. In this thesis, Iterative Fitting Approach to cr-MREPT is developed for investigating the possibility of elimination of LCF artifact. In this method, forward problem of obtaining magnetic eld with the given electrical properties inside the region of interest is solved iteratively and electrical properties are updated at each iteration until the di erence between the solution of the forward problem and the measured magnetic eld is small. Forward problem is a di usion convection reaction partial di erential equation and the solution for the magnetic eld is obtained by the Finite Di erence Method. By using the norm of the difference between the solution of the forward problem and the measured magnetic eld, electrical properties are obtained via Gauss-Newton method. Obtaining electrical property updates at each iteration, is not a well conditioned problem therefore Tikhonov and Total Variation regularizations are implemented to solve this problem. For the realization of the Total Variation regularization, Primal Dual Interior Point Method (PDIPM) is used. Using the COMSOL ...