8 papers
Product-of-Gaussian-Mixture Diffusion Models for Joint Nonlinear MRI Reconstruction
Laurenz Nagler, Martin Zach, Thomas Pock
Recently, diffusion models have attracted considerable attention for magnetic resonance image reconstruction due to their high sample quality. However, most existing methods rely o…
Forward-KL Convergence of Time-Inhomogeneous Langevin Diffusions
Andreas Habring, Martin Zach
Many practical samplers rely on time-dependent drifts -- often induced by annealing or tempering schedules -- to improve exploration and stability. This motivates a unified non-asy…
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…
Computation of a Consistent System Matrix for Cone-beam Computed Tomography
Josef Simbrunner, Clemens Krenn, Martin Zach +1
We propose a method for the computation of a consistent system matrix for two- and three-dimensional cone-beam computed tomography (CT). The method relies on the decomposition of t…
A Statistical Benchmark for Diffusion Posterior Sampling Algorithms
Martin Zach, Youssef Haouchat, Michael Unser
We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms for Bayesian linear inverse problems. The benchmark synthesizes signals from sparse Lévy-proce…
Energy-based models for inverse imaging problems
Andreas Habring, Martin Holler, Thomas Pock +1
In this chapter we provide a thorough overview of the use of energy-based models (EBMs) in the context of inverse imaging problems. EBMs are probability distributions modeled via G…