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Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging…
Deep learning models have proven to be exceptionally useful in performing many machine learning tasks. However, for each new dataset, choosing an effective size and structure of the model can be a time-consuming process of trial and error.…
Magnetic Resonance Imaging (MRI) is a critical tool in modern medical diagnostics, yet its prolonged acquisition time remains a critical limitation, especially in time-sensitive clinical scenarios. While undersampling strategies can…
This article is a direct continuation of [1] where we begun the study of the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator.…
Active development is taking place in reconfigurable and static metasurfaces that control and optimize reflections. However, existing designs typically only optimize reflections from the metasurface panels, neglecting interference with…
Diffusion Probabilistic Models (DPMs) have recently been employed for image deblurring, formulated as an image-conditioned generation process that maps Gaussian noise to the high-quality image, conditioned on the blurry input.…
We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e. pseudosymmetic matrices). The pseudosymmetric structure of the matrix is preserved in the spectral…
We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large…
Despite the tremendous progresses in wavefront control through or inside complex scattering media, several limitations prevent reaching practical feasibility for nonlinear imaging in biological tissues. While the optimization of nonlinear…
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…
This paper is concerned with the spectral properties of matrices associated with linear filters for the estimation of the underlying trend of a time series. The interest lies in the fact that the eigenvectors can be interpreted as the…
In this work, we study the spectral form factor of random matrix models which exhibit a large number of degenerate ground states accompanied by a macroscopic gap in the spectrum. The central aim of this work is to understand how the…
We describe inverse scattering for the matrix Schroedinger operator with general selfadjoint boundary conditions at the origin using the Marchenko equation. Our approach allows the recovery of the potential as well as the boundary…
Metasurfaces enable powerful control of electromagnetic waves using subwavelength planar structures, but their deeply subwavelength periodicity typically suppresses propagating diffraction orders, which limits the number of available…
A deep image compression scheme is proposed in this paper, offering the state-of-the-art compression efficiency, against the traditional JPEG, JPEG2000, BPG and those popular learning based methodologies. This is achieved by a novel…
In this paper, we study the inverse scattering problem for a class of signals that have a compactly supported reflection coefficient. The problem boils down to the solution of the Gelfand-Levitan-Marchenko (GLM) integral equations with a…
The problem of finding boundary conditions for fastening of a ring membrane, which are inaccessible for direct observation from the natural frequencies of its flexural oscillations, is considered. Two theorems on the uniqueness of this…
Signal reconstruction is a challenging aspect of computational imaging as it often involves solving ill-posed inverse problems. Recently, deep feed-forward neural networks have led to state-of-the-art results in solving various inverse…
Spectral projectors and the reflectors derived from them are basic objects in numerical linear algebra. This paper studies the prescribed-index reflector I-2P_k, where P_k is the spectral projector associated with the first k eigenvectors…
Remote sensing images are essential for many applications of the earth's sciences, but their quality can usually be degraded due to limitations in sensor technology and complex imaging environments. To address this, various remote sensing…