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The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results on smooth…
We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first-order systems and all second-order scalar operators. In…
We prove certain $L^p$ estimates ($1<p<\infty$) for non-isotropic singular integrals along surfaces of revolution. As an application we obtain $L^p$ boundedness of the singular integrals under a sharp size condition on their kernels.
We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial…
In this paper we will show how to construct holomorphic L^{p}-functions on unbranched coverings of strongly pseudoconvex manifolds. Also, we prove some extension and approximation theorems for such functions.
Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent…
The goal of this note is to give, at least for a restricted range of indices, a short proof of homogeneous commutator estimates for fractional derivatives of a product, using classical tools. Both $L^{p}$ and weighted $L^{p}$ estimates can…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (=a finite union of hyperplanes) whose Levi-Civita connection is of Dunkl…
Ptychography is a data-intensive computational imaging technique that achieves high spatial resolution over large fields of view. The technique involves scanning a coherent beam across overlapping regions and recording diffraction patterns.…
We prove new concentration estimates for random variables that are functionals of a Poisson measure defined on a general measure space. Our results are specifically adapted to geometric applications, and are based on a pervasive use of a…
We prove $l^p$-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of $p$ in all dimensions $n\ge 2$.
We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with very high…
Very recently, \v{S}pakula and Tikuisis provide a new characterisation of (uniform) Roe algebras via quasi-locality when the underlying metric spaces have straight finite decomposition complexity. In this paper, we improve their method to…
We propose an algorithm for robust recovery of the spherical harmonic expansion of functions defined on the d-dimensional unit sphere $\mathbb{S}^{d-1}$ using a near-optimal number of function evaluations. We show that for any $f \in…
In this paper, we extend the large sieve type estimates to sums involving pth powers of trigonometric polynomials. An approach to such estimates that does not rely on the usual L^2-technique is given. Our method is based on comparing the…
We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…
In the presence of occlusions and measurement noise, geometrically accurate scene reconstructions -- which fit the sensor data -- can still be physically incorrect. For instance, when estimating the poses and shapes of objects in the scene…
A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of…
In this paper, optimal $L^p-L^q$ estimates are obtained for operators which average functions over polynomial submanifolds, generalizing the $k$-plane transform. An important advance over previous work is that full $L^p-L^q$ estimates are…