Related papers: Neural-network-based regularization methods for in…
This paper presents an uncalibrated deep neural network framework for the photometric stereo problem. For training models to solve the problem, existing neural network-based methods either require exact light directions or ground-truth…
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…
The solution of inverse problems is of fundamental interest in medical and astronomical imaging, geophysics as well as engineering and life sciences. Recent advances were made by using methods from machine learning, in particular deep…
In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…
Training deep neural networks is known to require a large number of training samples. However, in many applications only few training samples are available. In this work, we tackle the issue of training neural networks for classification…
Recently, a large number of efficient deep learning methods for solving inverse problems have been developed and show outstanding numerical performance. For these deep learning methods, however, a solid theoretical foundation in the form of…
Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However,…
Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…
Numerous diffusion model (DM)-based methods have been proposed for solving inverse imaging problems. Among these, a recent line of work has demonstrated strong performance by formulating sampling as an optimization procedure that enforces…
In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…
Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity and low-rank. Unlike learned…
Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…
We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…
Predicting measurement outcomes from an underlying structure often follows directly from fundamental physical principles. However, a fundamental challenge is posed when trying to solve the inverse problem of inferring the underlying…
Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers,…
Efficient rendering of photo-realistic virtual worlds is a long standing effort of computer graphics. Modern graphics techniques have succeeded in synthesizing photo-realistic images from hand-crafted scene representations. However, the…
A broad class of problems at the core of computational imaging, sensing, and low-level computer vision reduces to the inverse problem of extracting latent images that follow a prior distribution, from measurements taken under a known…
Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation…
The recent development of diffusion models has led to significant progress in solving inverse problems by leveraging these models as powerful generative priors. However, challenges persist due to the ill-posed nature of such problems, often…