Related papers: The Kadison-Singer problem in discrepancy theory, …
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
We consider an overdetermined problem of Serrin-type with respect to an operator in divergence form with piecewise constant coefficients. We give sufficient condition for unique solvability near radially symmetric configurations by means of…
In this paper we survey a recent progress on continuous frames inspired by the solution of the Kadison-Singer problem by Marcus, Spielman, and Srivastava. We present an extension of Lyapunov's theorem for discrete frames due to Akemann and…
Multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. The MMV problems had been traditionally addressed either by sensor array signal processing or compressive…
In 2014 Adam Marcus, Daniel Spielman and Nikhil Srivastava used random vectors to prove a key discrepancy theorem and in so doing gave a positive answer to the long-standing Kadison-Singer Problem. In this paper we use Walsh matrices to…
We investigate the solution of the equation \partial_t E(x,t)-iD\partial_x^2 E(x,t)= \lambda |S(x,t)|^2 E(x,t)$, for x in a circle and S(x,t) a Gaussian stochastic field with a covariance of a particular form. It is shown that the coupling…
We discuss a method of solving $n^{th}$ order scalar ordinary differential equations by extending the ideas based on the Prelle-Singer (PS) procedure for second order ordinary differential equations. We also introduce a novel way of…
Compressive Sensing theory says that it is possible to reconstruct a measured signal if an enough sparse representation of this signal exists in comparison to the number of random measurements. This theory was applied to reconstruct signals…
We show that any $n\times m$ matrix $A$ can be approximated in operator norm by a submatrix with a number of columns of order the stable rank of $A$. This improves on existing results by removing an extra logarithmic factor in the size of…
In this work, we consider an extension to parabolic problems of the variational multiscale method with spectral approximation of the sub-scales. We first discretize in time using a finite difference scheme and second, apply the…
Is it possible to find the sparsest vector (direction) in a generic subspace $\mathcal{S} \subseteq \mathbb{R}^p$ with $\mathrm{dim}(\mathcal{S})= n < p$? This problem can be considered a homogeneous variant of the sparse recovery problem,…
We present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator's banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to…
The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical…
Conservative inference is a major concern in simulation-based inference. It has been shown that commonly used algorithms can produce overconfident posterior approximations. Balancing has empirically proven to be an effective way to mitigate…
The paper deals with the hitherto neglected topic of audio dequantization. It reviews the state-of-the-art sparsity-based approaches and proposes several new methods. Convex as well as non-convex approaches are included, and all the…
We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…
This paper solves the integral equation which describes the oscillating inhomogeneous string, by using a spectral expansion method in terms of Chebyshev polynomials. The result is compared with the solution of the corresponding differential…
We present an alternative pathway in the application of the variation improvement of ordinary perturbation theory exposed in [1] which can preserve the internal symmetries of a model by means of a time compactification.
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…