Naslov
Regularization of ill-posed inverse problem in ultrasound tomography

Autori
Carević, Anita

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Mjesto
Zagreb

Datum
21.12

Godina
2020

Stranica
123

Mentor
Ivan Slapničar ; Mohamed Almekkawy

Ključne riječi
Ill-posed inverse problem: Ultrasound tomography ; Tikhonov regularization ; Regularized total least squares method ; distorted Born iterative method

Sažetak
Ultrasound tomography (UT) is a medical imaging modality which can be used for the detection of breast cancer. One of the ways to solve the problem of UT is to use the distorted Born iterative method. In order for this method to provide a good solution, an ill-posed inverse problem must be solved within each iteration. In this dissertation, we regularize the inverse problem using direct spectral filtering methods. We show the advantage of using them in general form instead of standard, since employing modification of discrete version of first order derivative operator will provide additional regularization. The goal of the aforementioned methods is to minimize the influence of smaller (generalized) singular values, so the selection of the regularization parameter that is determining which of the values will be omitted is crucial to these methods. For this purpose we develop a new algorithm for choosing the regularization parameter that is, minimizing the residual and the error resulted from the noise of the measured data. In addition, we regularize the inverse problem using new forms of regularized total least squares where the existing problem is projected onto lower dimensional subspace. The dimension reduction is achieved by employing a generalized Krylov subspace expansion which results in significant decrease of computational time. In addition, the problem associated with finding the regularization parameter is avoided since an integrated parameter search inside the method is provided.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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