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We introduce a novel reflection-mode diffraction tomography technique that enables simultaneous recovery of forward and backward scattering information for high-resolution 3D refractive index reconstruction. Our technique works by imaging a…
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with $\alpha$-H\"older derivatives (for some $0<\alpha\leq 1$). The smooth approximation is given by means of an…
The proximinality of certain subspaces of spaces of bounded affine functions is proved. The results presented here are some linear versions of an old result due to Mazur. For the proofs we use some sandwich theorems of Fenchel's duality…
Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations…
In this paper, we propose a new algorithm combining the Douglas-Rachford (DR) algorithm and the Frank-Wolfe algorithm, also known as the conditional gradient (CondG) method, for solving the classic convex feasibility problem. Within the…
We study approximations to the Moreau envelope -- and infimal convolutions more broadly -- based on Laplace's method, a classical tool in analysis which ties certain integrals to suprema of their integrands. We believe the connection…
Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
We analyse the behaviour of the newly introduced cyclic Douglas-Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is…
Being able to see beyond the direct line of sight is an intriguing prospective and could benefit a wide variety of important applications. Recent work has demonstrated that time-resolved measurements of indirect diffuse light contain…
More than 40 years ago, Lions and Mercier introduced in a seminal paper the Douglas-Rachford algorithm. Today, this method is well recognized as a classical and highly successful splitting method to find minimizers of the sum of two (not…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
In recent years, the Douglas-Rachford splitting method has been shown to be effective at solving many non-convex optimization problems. In this paper we present a local convergence analysis for non-convex feasibility problems and show that…
Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
We motivate then formulate a novel variant of the near-field reflector problem and call it the near-field reflector problem with spatial restrictions. Let $O$ be an anisotropic point source of light and assume that we are given a bounded…
In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represents manifold data accurately while preserving the manifold's…
Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…
For linear and fully non-linear diffusion equations of Bellman-Isaacs type, we introduce a class of approximation schemes based on differencing and interpolation. As opposed to classical numerical methods, these schemes work for general…
In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…