Related papers: Sparse polynomial interpolation: sparse recovery, …
Much of the existing literature in sparse recovery is concerned with the following question: given a sparsity pattern and a corresponding regularizer, derive conditions on the dictionary under which exact recovery is possible. In this…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…
The sparse polynomial approximation of continuous functions has emerged as a prominent area of interest in function approximation theory in recent years. A key challenge within this domain is the accurate estimation of approximation errors.…
In this paper, we show a way to exploit sparsity in the problem data in a primal-dual potential reduction method for solving a class of semidefinite programs. When the problem data is sparse, the dual variable is also sparse, but the primal…
This paper studies the problem of exact localization of sparse (point or extended) objects with noisy data. The crux of the proposed approach consists of random illumination. Several recovery methods are analyzed: the Lasso, BPDN and the…
We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…
This paper studies the recovery of a superposition of point sources from noisy bandlimited data. In the fewest possible words, we only have information about the spectrum of an object in a low-frequency band bounded by a certain cut-off…
We propose a new technique for radio interferometry to obtain super-resolution full polarization images in all four Stokes parameters using sparse modeling. The proposed technique reconstructs the image in each Stokes parameter from the…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover…
We address the problem of super-resolution line spectrum estimation of an undersampled signal with block prior information. The component frequencies of the signal are assumed to take arbitrary continuous values in known frequency blocks.…
We present algorithms performing sparse univariate polynomial interpolation with errors in the evaluations of the polynomial. Based on the initial work by Comer, Kaltofen and Pernet [Proc. ISSAC 2012], we define the sparse polynomial…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as…
Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a "modular black box polynomial", e.g. via an algorithm to evaluate f at arbitrary integer points, modulo arbitrary positive integers.…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
We study superconvergence property of the linear finite element method with the polynomial preserving recovery (PPR) and Richardson extrapolation for the two dimensional Helmholtz equation. The $H^1$-error estimate with explicit dependence…