Related papers: A Unified Approach to Attractor Reconstruction

Recent years have witnessed the surge of asynchronous parallel (async-parallel) iterative algorithms due to problems involving very large-scale data and a large number of decision variables. Because of asynchrony, the iterates are computed…

We consider the iterative reconstruction of both the internal geometry and the values of an inhomogeneous acoustic refraction index through a piecewise constant approximation. In this context, we propose two enhancements intended to reduce…

One of the most successful approaches to modern high quality HDR-video capture is to use camera setups with multiple sensors imaging the scene through a common optical system. However, such systems pose several challenges for HDR…

Reconstructing the parameters that encode the influence between model variables based on time-series measurements represents an outstanding question in the theory of complex network-coupled systems. Here, we propose a solution to this…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…

Estimating the causal effect of a treatment or health policy with observational data can be challenging due to an imbalance of and a lack of overlap between treated and control covariate distributions. In the presence of limited overlap,…

Many real-world problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns in the field of computer vision. Recently, the alignment problem…

Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…

Despite the rapid advance of unsupervised anomaly detection, existing methods require to train separate models for different objects. In this work, we present UniAD that accomplishes anomaly detection for multiple classes with a unified…

Network reconstruction is the task of inferring the unseen interactions between elements of a system, based only on their behavior or dynamics. This inverse problem is in general ill-posed, and admits many solutions for the same…

This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a…

In dynamic MRI, sufficient time resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based image…

This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…

In human perception and cognition, a fundamental operation that brains perform is interpretation: constructing coherent neural states from noisy, incomplete, and intrinsically ambiguous evidence. The problem of interpretation is well…