Related papers: A regularized weighted least gradient problem for …
We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and…
Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…
We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise $\ell_1$ regularization to the free energy of the quantum system. Based on the…
In this paper, we are interested in the application to video segmentation of the discrete shape optimization problem involving the shape weighted perimeter and an additional term depending on a parameter. Based on recent works and in…
We propose a new joint image reconstruction method by recovering edge directly from observed data. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an $l_1$ minimization problem…
We study the possible regularization of collision solutions for one centre problems with a weak singularity. In the case of logarithmic singularities, we consider the method of regularization via smoothing of the potential. With this…
The inversion of electromagnetic induction data to a conductivity profile is an ill-posed problem. Regularization improves the stability of the inversion and, based on Occam's razor principle, a smoothing constraint is typically used.…
Depth estimation is a fundamental problem for light field photography applications. Numerous methods have been proposed in recent years, which either focus on crafting cost terms for more robust matching, or on analyzing the geometry of…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
We study the variational inference problem of minimizing a regularized R\'enyi divergence over an exponential family. We propose to solve this problem with a Bregman proximal gradient algorithm. We propose a sampling-based algorithm to…
Motivated by many applications, optimal control problems with integer controls have recently received a significant attention. Some state-of-the-art work uses perimeter-regularization to derive stationarity conditions and trust-region…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
We study the numerical reconstruction problem in acousto-electric tomography (AET) of recovering the conductivity distribution in a bounded domain from multiple interior power density data. The Two-Point-Gradient-$\Theta$ (TPG-$\Theta$) in…
Reconstructing under-sampled k-space measurements in Compressed Sensing MRI (CS-MRI) is classically solved with regularized least-squares. Recently, deep learning has been used to amortize this optimization by training reconstruction…
Transmission Electron Microscopy enables high-resolution imaging of materials, but the resulting images are difficult to interpret directly. One way to address this is exit wave reconstruction, i.e., the recovery of the complex-valued…
Several regularization methods have recently been introduced which force the latent activations of an autoencoder or deep neural network to conform to either a Gaussian or hyperspherical distribution, or to minimize the implicit rank of the…
Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…
Equations describing the complete series of image charges for a system of conducting spheres are presented. The method of image charges, originally described by J. C. Maxwell in 1873, has been and continues to be a useful method for solving…
We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000)…