Related papers: On Regularisation of Coherent Imagery with Proxima…
We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…
In this paper, we investigate regularization of linear inverse problems with irregular noise. In particular, we consider the case that the noise can be preprocessed by certain adjoint embedding operators. By introducing the consequent…
The Tianlai cylinder pathfinder is a radio interferometer array to test 21 cm intensity mapping techniques in the post-reionization era. It works in passive drift scan mode to survey the sky visible in the northern hemisphere. To deal with…
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with…
Regularisation is commonly used in iterative methods for solving imaging inverse problems. Many algorithms involve the evaluation of the proximal operator of the regularisation term in every iteration, leading to a significant computational…
The object of this work is to design an adequate regularization for the problem of recovering missing Fourier coefficients, particularly in some non standard situations were low frequency coefficients are lost. In the framework of non-local…
We give an effective solution to the regularized optimization problem $g (\boldsymbol{x}) + h (\boldsymbol{x})$, where $\boldsymbol{x}$ is constrained on the unit sphere $\Vert \boldsymbol{x} \Vert_2 = 1$. Here $g (\cdot)$ is a smooth cost…
We propose a sparse reconstruction framework for solving inverse problems. Opposed to existing sparse regularization techniques that are based on frame representations, we train an encoder-decoder network by including an $\ell^1$-penalty.…
We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…
Pretrained segmentation models for cardiac magnetic resonance imaging (MRI) struggle to generalize across different imaging sequences due to significant variations in image contrast. These variations arise from changes in imaging protocols,…
The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…
Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to evaluate the integral accurately at points on or near the…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a…
This paper presents measures to reduce the computation time of automotive synthetic aperture radar (SAR) imaging to achieve real-time capability. For this, the image formation, which is based on the Back-Projection algorithm, was thoroughly…
The globally optimal robust adaptive beamforming (RAB) solution is studied for worst-case signal-to-interference-plus-noise ratio (SINR) maximization (the maximin SINR problem) under convex and closed uncertainty sets for the desired signal…
Local reconstruction analysis (LRA) is a powerful and flexible technique to study images reconstructed from discrete generalized Radon transform (GRT) data, $g=\mathcal R f$. The main idea of LRA is to obtain a simple formula to accurately…
When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…
The traditional approaches to computerized tomography (CT) depend on the samples of Radon transform at multiple angles. In optics, the real time imaging requires the reconstruction of an object by the samples of Radon transform at a single…
In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural…