arXiv research

Transfer learning improves lensless imaging through scattering media with fewer samples.

This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm for random Gaussian measurements (practically relevant in imaging through scatt…

Study travel time tomography for transversely isotropic media using modified pseudodifferential calculus.

One of the biggest challenges in the field of biomedical imaging is the comprehension and the exploitation of the photon scattering through disordered media. Many studies have pursued the solution to this puzzle, achieving light-focusing control or reconstructing images in complex media. In the present work, we investi…

Solves a challenging problem in imaging and communication.

We prove stability and exponential convergence of the Perfectly Matched Layer (PML) method for acoustic scattering on manifolds with axial analytic quasicylindrical ends. These manifolds model long-range geometric perturbations (e.g. bending or stretching) of tubular waveguides filled with homogeneous or inhomogeneous …

We present a riemannian structure on the disk that has a remarkably rich structure. Geodesics are hypocycloids and the (negative of the) laplacian has integer spectrum with multiplicity the Dirichlet divisor function. Eigenfunctions of the laplacian are orthogonal polynomials naturally suited to the analysis of acousti…

Linear problems appear in a variety of disciplines and their application for the transmission matrix recovery is one of the most stimulating challenges in biomedical imaging. Its knowledge turns any random media into an optical tool that can focus or transmit an image through disorder. Here, converting an input-output …

New model predicts radiative properties of nanoparticle layers with high accuracy and uncertainty.

Consider a broken geodesics $α([0,l])$ on a compact Riemannian manifold $(M,g)$ with boundary of dimension $n\geq 3$. The broken geodesics are unions of two geodesics with the property that they have a common end point. Assume that for every broken geodesic $α([0,l])$ starting at and ending to the boundary $\partial M$…

AI model predicts stock prices using social media data and hybrid neural networks.

Combines deep learning and iterative methods for robust phase retrieval.

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be trained, which in imaging applications implicates prohibitively expensive collectio…

Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional phase retrieval …

New equations for Cosserat media motions derived from bundle automorphisms.

We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplect…

We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probabil…

Paper explains scattering diagrams' role in mirror symmetry.

New method uses broken scattering to uniquely identify Finsler manifolds.

GSAN learns adaptive node representations using geometric scattering and attention.

New method learns soliton dynamics from scattering data without assuming known equations.

Unified graph scattering transforms improve theoretical properties of graph neural networks.

Scattering representations simplify SBI for images without extra compression.

The paper establishes scattering theory for wave equations on Schwarzschild spacetime.

Paper develops formulas for shape derivatives in wave scattering.

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest in geometric deep learning, which aims to generalize ConvNets to manifold and gra…

Study scattering rigidity on stationary manifolds using geodesics.

This article asks how planning scholarship may effectively gain impact in planning practice through media exposure. In liberal democracies the public sphere is dominated by mass media. Therefore, working with such media is a prerequisite for effective public impact of planning research. Using the example of megaproject…

MODWST improves classification tasks with wavelet scattering.

Study on scattering geodesics on modular surface and their sojourn times.

Scattering theory on Riemann surfaces with explicit matrix and generalized period mappings.

Study on recovering Lorentzian metrics from scattering data.

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric…

Study compares sentiment spillover networks from news and social media in tech companies.

As a highlighting research topic in the multimedia area, cross-media retrieval aims to capture the complex correlations among multiple media types. Learning better shared representation and distance metric for multimedia data is important to boost the cross-media retrieval. Motivated by the strong ability of deep neura…

The paper introduces new uniformity and homogeneity concepts for Cosserat media.

Bayesian Scattering offers a simple baseline for image data uncertainty.

Scattering theory for linearised gravity on Schwarzschild black hole exterior.

We construct continuous families of scattering manifolds with the same scattering phase. The manifolds are compactly supported metric perturbations of Euclidean $\mathbf{R}^{n}$ for $n\geq8$. The metric perturbation may have arbitrarily small support.

Social media enhances or diminishes scientific status, depending on usage.

Scattering theory for harmonic one-forms on Riemann surfaces.

Paper shows how scattering maps of Schrödinger equations relate to metrics.

The problem of recovering the asymptotics of a short range perturbation of the Euclidean metric on R^n from fixed energy scattering data is studied. It is shown that if two such metrics, g1, g2, have scattering data at some fixed energy which are equal up to smoothing, then there exists a diffeomorphism ψ`fixing infini…

Scattering theory developed for linearised gravity near Schwarzschild black hole.

Establishes scattering theory for de Sitter vacuum solutions in even dimensions.

Media tone around earnings announcements predicts stock returns.

We develop a geometric scattering theory for a geometrically finite group acting on (a vector bundle over) a symmetric space of negative curvature. In particular, we obtain the meromorphic continuation of Eisenstein series and scattering matrices and their functional equations.

We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions where the asymptotic curvature is sufficiently negative. The scattering matrix i…