8 papers
Splines and Operators: Part II - Resolution of Inverse Problems
Michael Unser
We present a unified treatment of the data-fitting problems with quadratic (Hilbertian) regularization that arise in approximation theory, machine learning, engineering, and statis…
Splines and Operators: Part I - Admissibility and Native Spaces
Michael Unser
The variational theory of splines requires a native space: a Hilbert space over which the regularization energy is well defined and the minimum-energy in…
Generalized Splines and Gaussian Processes
Michael Unser
For finite-dimensional linear inverse problems where the variables are Gaussian, it is well-known that the minimum-mean-square error estimator takes the form of a regularized least…
Variational Tensor-Product Splines
Vincent Guillemet, Michael Unser
Multidimensional continuous-domain inverse problems are often solved by the minimization of a loss functional, formed as the sum of a data fidelity and a regularization. In this wo…
Sampling in BV-Type Spaces
Vincent Guillemet, Michael Unser
The sampling of functions of bounded variation (BV) is a long-standing problem in op- timization. The ability to sample such functions has relevance in the field of variational inv…
Mixed-Derivative Total Variation
Vincent Guillemet, Michael Unser
The formulation of norms on continuous-domain Banach spaces with exact pixel-based discretization is advantageous for solving inverse problems (IPs). In this paper, we investigate…
Adaptive Vector-Valued Splines for the Resolution of Inverse Problems
Vincent Guillemet, Michaël Unser
We introduce a general framework for the reconstruction of vector-valued functions from finite and possibly noisy data, acquired through a known measurement operator. The reconstru…
The Gaussian Latent Machine: Efficient Prior and Posterior Sampling for Inverse Problems
Muhamed Kuric, Martin Zach, Andreas Habring +2
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We sho…