SIAM Journal on Applied Mathematics
Singularities of the X-ray transform and limited data tomography in R2 and R3
SIAM Journal on Mathematical Analysis
SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
Mathematical methods in image reconstruction
Mathematical methods in image reconstruction
The mathematics of computerized tomography
The mathematics of computerized tomography
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data
Journal of Computational Physics
A general local reconstruction approach based on a truncated Hilbert transform
Journal of Biomedical Imaging
Limited Data X-Ray Tomography Using Nonlinear Evolution Equations
SIAM Journal on Scientific Computing
A general total variation minimization theorem for compressed sensing based interior tomography
Journal of Biomedical Imaging
Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization
Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A curve evolution approach to object-based tomographic reconstruction
IEEE Transactions on Image Processing
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In this article the Mumford-Shah-like method of [R. Ramlau and W. Ring, J. Comput. Phys., 221 (2007), pp. 539-557] for complete tomographic data is generalized and applied to limited angle and region of interest tomography data. With the Mumford-Shah-like method, one reconstructs a piecewise constant function and simultaneously a segmentation from its (complete) Radon transform data. For limited data, the ability of the Mumford-Shah-like method to find a segmentation, and by that the singularity set of a function, is exploited. The method is applied to generated data from a torso phantom. The results demonstrate the performance of the method in reconstructing the singularity set, the density distribution itself for limited angle data, and also some quantitative information about the density distribution for region of interest data. As a second example limited angle region of interest tomography is considered as a simplified model for electron tomography (ET). For this problem we combine Lambda tomography and the Mumford-Shah-like method. The combined method is applied to simulated ET data.