4 citations · 8 across the 6 of their papers we have counts for
6 papers
Neural network parametrized level sets for image segmentation
Otmar Scherzer, Cong Shi, Thi Lan Nhi Vu
Chan-Vese algorithms have proven to be a first-class method for image segmentation. Early implementations used level set methods with a pixelwise representation of the level set fu…
Classification with neural networks with quadratic decision functions
Leon Frischauf, Otmar Scherzer, Cong Shi
Neural networks with quadratic decision functions have been introduced as alternatives to standard neural networks with affine linear ones. They are advantageous when the objects o…
Quadratic neural networks for solving inverse problems
Leon Frischauf, Otmar Scherzer, Cong Shi
In this paper we investigate the solution of inverse problems with neural network ansatz functions with generalized decision functions. The relevant observation for this work is th…
Density Matrix Reconstructions in Ultrafast Transmission Electron Microscopy: Uniqueness, Stability, and Convergence Rates
Cong Shi, Claus Ropers, Thorsten Hohage
In the recent paper [17] the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem…
Reconstruction formulas for Photoacoustic Imaging in Attenuating Media
Otmar Scherzer, Cong Shi
In this paper we study the problem of photoacoustic inversion in a weakly attenuating medium. We present explicit reconstruction formulas in such media and show that the inversion…
Singular Values of the Attenuated Photoacoustic Imaging Operator
Peter Elbau, Otmar Scherzer, Cong Shi
We analyse the ill-posedness of the photoacoustic imaging problem in the case of an attenuating medium. To this end, we introduce an attenuated photoacoustic operator and determine…