6 papers
Spectral Function Space Learning and Numerical Linear Algebra Networks for Solving Linear Inverse Problems
Andrea Aspri, Leon Frischauf, Otmar Scherzer
We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of image…
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…
Universal approximation properties of shallow quadratic neural networks
Leon Frischauf, Otmar Scherzer, Cong Shi
In this paper we study shallow neural network functions which are linear combinations of compositions of activation and quadratic functions, replacing standard affine linear functi…
Data driven reconstruction using frames and Riesz bases
Andrea Aspri, Leon Frischauf, Yury Korolev +1
We study the problem of regularization of inverse problems adopting a purely data driven approach, by using the similarity to the method of regularization by projection. We provide…
Diffusion Tensor Regularization with Metric Double Integrals
Leon Frischauf, Melanie Melching, Otmar Scherzer
In this paper we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued…