Convergent Bregman Plug-and-Play Image Restoration for Poisson Inverse Problems

Plug-and-Play (PnP) methods are efficient iterative algorithms for solving ill-posed image inverse problems. PnP methods are obtained by using deep Gaussian denoisers instead of the proximal operator or the gradient-descent step within proximal algorithms. Current PnP schemes rely on data-fidelity terms that have either Lipschitz gradients or closed-form proximal operators, which is not applicable to Poisson inverse problems. Based on the observation that the Gaussian noise is not the adequate noise model in this setting, we propose to generalize PnP using theBregman Proximal Gradient (BPG) method. BPG replaces the Euclidean distance with a Bregman divergence that can better capture the smoothness properties of the problem. We introduce the Bregman Score Denoiser specifically parametrized and trained for the new Bregman geometry and prove that it corresponds to the proximal operator of a nonconvex potential. We propose two PnP algorithms based on the Bregman Score Denoiser for solving Poisson inverse problems. Extending the convergence results of BPG in the nonconvex settings, we show that the proposed methods converge, targeting stationary points of an explicit global functional. Experimental evaluations conducted on various Poisson inverse problems validate the convergence results and showcase effective restoration performance

Volumetric MRI Reconstruction from 2D Slices in the Presence of Motion

Despite recent advances in acquisition techniques and reconstruction algorithms, magnetic resonance imaging (MRI) remains challenging in the presence of motion. To mitigate this, ultra-fast two-dimensional (2D) MRI sequences are often used in clinical practice to acquire thick, low-resolution (LR) 2D slices to reduce in-plane motion. The resulting stacks of thick 2D slices typically provide high-quality visualizations when viewed in the in-plane direction. However, the low spatial resolution in the through-plane direction in combination with motion commonly occurring between individual slice acquisitions gives rise to stacks with overall limited geometric integrity. In further consequence, an accurate and reliable diagnosis may be compromised when using such motion-corrupted, thick-slice MRI data. This thesis presents methods to volumetrically reconstruct geometrically consistent, high-resolution (HR) three-dimensional (3D) images from motion-corrupted, possibly sparse, low-resolution 2D MR slices. It focuses on volumetric reconstructions techniques using inverse problem formulations applicable to a broad field of clinical applications in which associated motion patterns are inherently different, but the use of thick-slice MR data is current clinical practice. In particular, volumetric reconstruction frameworks are developed based on slice-to-volume registration with inter-slice transformation regularization and robust, complete-outlier rejection for the reconstruction step that can either avoid or efficiently deal with potential slice-misregistrations. Additionally, this thesis describes efficient Forward-Backward Splitting schemes for image registration for any combination of differentiable (not necessarily convex) similarity measure and convex (not necessarily smooth) regularization with a tractable proximal operator. Experiments are performed on fetal and upper abdominal MRI, and on historical, printed brain MR films associated with a uniquely long-term study dating back to the 1980s. The results demonstrate the broad applicability of the presented frameworks to achieve robust reconstructions with the potential to improve disease diagnosis and patient management in clinical practice

Network Calculus with Flow Prolongation -- A Feedforward FIFO Analysis enabled by ML

The derivation of upper bounds on data flows' worst-case traversal times is an important task in many application areas. For accurate bounds, model simplifications should be avoided even in large networks. Network Calculus (NC) provides a modeling framework and different analyses for delay bounding. We investigate the analysis of feedforward networks where all queues implement First-In First-Out (FIFO) service. Correctly considering the effect of data flows onto each other under FIFO is already a challenging task. Yet, the fastest available NC FIFO analysis suffers from limitations resulting in unnecessarily loose bounds. A feature called Flow Prolongation (FP) has been shown to improve delay bound accuracy significantly. Unfortunately, FP needs to be executed within the NC FIFO analysis very often and each time it creates an exponentially growing set of alternative networks with prolongations. FP therefore does not scale and has been out of reach for the exhaustive analysis of large networks. We introduce DeepFP, an approach to make FP scale by predicting prolongations using machine learning. In our evaluation, we show that DeepFP can improve results in FIFO networks considerably. Compared to the standard NC FIFO analysis, DeepFP reduces delay bounds by 12.1% on average at negligible additional computational cost