Investigating molecular transport in the human brain from MRI with physics-informed neural networks
In recent years, a plethora of methods combining neural networks and partial differential
equations have been developed. A widely known example are physics-informed neural …
equations have been developed. A widely known example are physics-informed neural …
Bilevel methods for image reconstruction
C Crockett, JA Fessler - Foundations and Trends® in Signal …, 2022 - nowpublishers.com
This review discusses methods for learning parameters for image reconstruction problems
using bilevel formulations. Image reconstruction typically involves optimizing a cost function …
using bilevel formulations. Image reconstruction typically involves optimizing a cost function …
Multimodal 4DVarNets for the reconstruction of sea surface dynamics from SST-SSH synergies
The space-time reconstruction of sea surface dynamics from satellite observations is a
challenging inverse problem due to the associated irregular sampling. Satellite altimetry …
challenging inverse problem due to the associated irregular sampling. Satellite altimetry …
[HTML][HTML] A non-convex denoising model for impulse and Gaussian noise mixture removing using bi-level parameter identification
We propose a new variational framework to remove a mixture of Gaussian and impulse
noise from images. This framework is based on a non-convex PDE-constrained with a …
noise from images. This framework is based on a non-convex PDE-constrained with a …
Image recovery via transform learning and low-rank modeling: The power of complementary regularizers
Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their
usefulness in various image/video processing applications. Patch-based methods exploit …
usefulness in various image/video processing applications. Patch-based methods exploit …
An optimal control approach for determining the source term in fractional diffusion equation by different cost functionals
This work is devoted to the mathematical analysis of an inverse source problem governed by
a time-fractional diffusion equation. The aims of this paper are to identify the source function …
a time-fractional diffusion equation. The aims of this paper are to identify the source function …
A weighted parameter identification PDE-constrained optimization for inverse image denoising problem
This paper treats the inverse denoising problem which aims to compute simultaneously the
clean image and the weighting parameter λ. The formulated denoising problem is posed …
clean image and the weighting parameter λ. The formulated denoising problem is posed …
An improved spatially controlled reaction–diffusion equation with a non-linear second order operator for image super-resolution
In this work, we introduce an efficient second-order reaction–diffusion (RD) equation for
noise removal and image super-resolution. The main idea is to decompose the image into …
noise removal and image super-resolution. The main idea is to decompose the image into …
Bilevel optimization methods in imaging
JC De los Reyes, D Villacís - … of Mathematical Models and Algorithms in …, 2022 - Springer
Optimization techniques have been widely used for image restoration tasks, as many
imaging problems may be formulated as minimization ones with the recovered image as the …
imaging problems may be formulated as minimization ones with the recovered image as the …
Analysis and automatic parameter selection of a variational model for mixed Gaussian and salt-and-pepper noise removal
L Calatroni, K Papafitsoros - Inverse Problems, 2019 - iopscience.iop.org
We analyse a variational regularisation problem for mixed noise removal that has been
recently proposed in Calatroni et al (2017 SIAM J. Imaging Sci. 10 1196–233). The data …
recently proposed in Calatroni et al (2017 SIAM J. Imaging Sci. 10 1196–233). The data …