Zobrazeno 1 - 10
of 505
pro vyhledávání: '"Scherzer, O."'
Publikováno v:
Inverse Problems and Imaging 1 (2007), no. 3, 507-523
In part I we introduced modified Landweber-Kaczmarz methods and have established a convergence analysis. In the present work we investigate three applications: an inverse problem related to thermoacoustic tomography, a nonlinear inverse problem for s
Externí odkaz:
http://arxiv.org/abs/2011.09913
Publikováno v:
Inverse Problems and Imaging 1 (2007), no. 2, 289-298
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and incorporating
Externí odkaz:
http://arxiv.org/abs/2011.09893
Autor:
Leitao, A., Scherzer, O.
Publikováno v:
Inverse Problems 19 (2003), no. 1, L1-L11
We consider regularization methods based on the coupling of Tikhonov regularization and projection strategies. From the resulting constraint regularization method we obtain level set methods in a straight forward way. Moreover, we show that this appr
Externí odkaz:
http://arxiv.org/abs/2011.07178
Publikováno v:
SIAM Journal on Numerical Analysis 43 (2005), no. 2, 767-786
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a novel concep
Externí odkaz:
http://arxiv.org/abs/2011.06999
Autor:
Hofmann, B., Scherzer, O.
The characterization of the local ill-posedness and the local degree of nonlinearity are of particular importance for the stable solution of nonlinear ill-posed problems. We present assertions concerning the interdependence between the ill-posedness
In this paper we propose an algorithm for the detection of edges in images that is based on topological asymptotic analysis. Motivated from the Mumford--Shah functional, we consider a variational functional that penalizes oscillations outside some ap
Externí odkaz:
http://arxiv.org/abs/1306.2466
Autor:
Widlak, T., Scherzer, O.
Hybrid imaging techniques utilize couplings of physical modalities -- they are called hybrid, because, typically, the excitation and measurement quantities belong to different modalities. Recently there has been an enormous research interest in this
Externí odkaz:
http://arxiv.org/abs/1112.2958
Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in
Externí odkaz:
http://arxiv.org/abs/1004.2838
Publikováno v:
Commun. Math. Sci. 7(3), pp. 665-678 (2009)
A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of circular inte
Externí odkaz:
http://arxiv.org/abs/0809.2052
Publikováno v:
IEEE Transactions on Medical Imaging 28(11) pp. 1727-1735 (2009)
Fourier reconstruction algorithms significantly outperform conventional back-projection algorithms in terms of computation time. In photoacoustic imaging, these methods require interpolation in the Fourier space domain, which creates artifacts in rec
Externí odkaz:
http://arxiv.org/abs/0808.3510