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A Mollification Approach for Inverting the Spherical Mean Radon Transform
SIAM Journal on Applied Mathematics, 2011The filtered backprojection algorithm is still one of the most important reconstruction methods in computed tomography. It is based on explicit formulas for recovering mollified versions of the original unknown function. In this paper, we derive such formulas for the spherical mean Radon transform with centers restricted to the boundary of a ball.
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Mollification of Viscosity Solutions and Semiconvexity
2014This chapter deals with the mollification of viscosity solutions and semiconvexity. The apt mollification scheme for viscosity solutions which respects our generalised derivatives, namely the semi-jets \(\fancyscript{J}^{2,\pm }\), is 1-sided. It is crucial to invent suitable regularisations of viscosity solutions in order to be able to manipulate ...
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Mollification along the Coarse Scale Flow
2017This chapter shows how to construct the appropriate mollification of the Reynolds stress along the coarse scale flow. Unlike the velocity field, which was only mollified in the spatial variables and which earned its time-regularity through the Euler-Reynolds equation, the Reynolds stress must be mollified in both space and time. Mollification along the
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The Mollification Method and the Numerical Solution of an Inverse Heat Conduction Problem
SIAM Journal on Scientific and Statistical Computing, 1981We show how the inverse problem can be stabilized by reconstructing a slightly “blurred” image of the unknowns. The numerical problem is solved with an absolute minimum of computation and the proposed method is favorably compared against others commonly in use.
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A Mollification Scheme for Task and Motion Planning.
CoRR, 2023Jimmy Envall, Roi Poranne, Stelian Coros
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