相关论文: Reconstructing Point Sets from Distance Distributi…

We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a…

We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show…

Reconstructing complex networks from measurable data is a fundamental problem for understanding and controlling collective dynamics of complex networked systems. However, a significant challenge arises when we attempt to decode structural…

We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears…

Recovering a stochastic process from noisy ensembles of single particle trajectories (SPTs) is resolved here using the Langevin equation as a model. The massive redundancy contained in SPTs data allows recovering local parameters of the…

Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities. In recent years, the use of randomized methods to sample from the vast space…

We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…

We address the inverse problem of reconstructing both the structure and dynamics of a network from mean-field measurements, which are linear combinations of node states. This setting arises in applications where only a few aggregated…

We present a new object representation, called Dense RepPoints, that utilizes a large set of points to describe an object at multiple levels, including both box level and pixel level. Techniques are proposed to efficiently process these…

We consider simultaneously identifying the membership and locations of point sources that are convolved with different band-limited point spread functions, from the observation of their superpositions. This problem arises in…

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…

In the pooled data problem we are given a set of $n$ agents, each of which holds a hidden state bit, either $0$ or $1$. A querying procedure returns for a query set the sum of the states of the queried agents. The goal is to reconstruct the…

Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions,…

We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction…

Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…

We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…

We consider the problem of reconstructing wideband frequency spectra from distributed, compressive measurements. The measurements are made by a network of nodes, each independently mixing the ambient spectra with low frequency, random…

In this Letter, we address the longstanding challenge of how to reconstruct links in directed networks from measurements, and present a general method that makes use of a noise-induced relation between network structure and both the…

In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method…

Weak lensing convergence maps - upon which higher order statistics can be calculated - can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed…