engleski

Regularization of Inverse Scattering Problem in Ultrasound Tomography

Most fi nite dimensional inverse problems that arise in applications are ill-posed. However, choosing a proper regularization algorithm depends on the problem itself. Here, our focus is on the ultrasound tomography, more precisely, a distorted Born iterative (DBI) method as a powerful way for reconstructing an ultrasound image. The inverse scattering part of DBI, denoted with Xy = b, is ill-posed, making it sensitive to errors. A regularization algorithm is necessary to ensure convergence of the DBI and produce a high quality ultrasound image. We are presenting the advantages of algorithms that employ generalized singular value decomposition (GSVD) of matrix pair (X ; L) over algorithms with SVD of matrix X for regularization of problem Xy = b in DBI. The usage of matrix L provides additional regularization by smoothing the noise. Usually, a discrete version of fi rst or second order derivative operator could be used. In addition, since the regularization properties of algorithms depend largely on the choice of good regularization parameter, we are proposing a new way for their determination suited for this problem. Numerical simulations for reconstruction of images using aforementioned methods are presented.

Inverse problem ; regularization

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