Related papers: Nonlinear reconstruction
Visualizing the high-redshift Universe is difficult due to the dearth of available data; however, the Lyman-alpha forest provides a means to map the intergalactic medium at redshifts not accessible to large galaxy surveys. Large-scale…
We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a…
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…
Diffusion models (DMs) have demonstrated remarkable ability to generate diverse and high-quality images by efficiently modeling complex data distributions. They have also been explored as powerful generative priors for signal recovery,…
We study an elastic Calderon-type inverse problem: recover the mass density $\rho(x)$ in a bounded domain $\Omega\subset\mathbb{R}^3$ from the Neumann-to-Dirichlet map associated with the isotropic Lam\'e system…
A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
We reconstruct a closed denoised curve from an unstructured and highly noisy 2D point cloud. Our proposed method uses a two- pass approach: Previously recovered manifold connectivity is used for ordering noisy samples along this manifold…
High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…
Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. Classical approaches to this problem assume a small number of feature points and,…
In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…
We introduce a numerical framework for reconstructing the potential in two dimensional semilinear elliptic PDEs with power type nonlinearities from the nonlinear Dirichlet to Neumann map. By applying higher order linearization method, we…
Machine learning often needs to model density from a multidimensional data sample, including correlations between coordinates. Additionally, we often have missing data case: that data points can miss values for some of coordinates. This…
In this paper, we show numerically that a symmetric Earth matter density profile can, in principle, be reconstructed from a single baseline energy spectrum up to a certain precision. For the numerical evaluations in the high dimensional…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…
The uncovering of the large-scale structure that is hidden in the Zone of Avoidance is essential to our quest for the understanding of the dynamics of the nearby universe. Dedicated and sophisticated observations of the Zone of Avoidance…
We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…
Personalized cardiac diagnostics require accurate reconstruction of myocardial displacement fields from sparse clinical imaging data, yet current methods often demand intrusive access to computational models. In this work, we apply the…
The peculiar velocity field of the local Universe provides direct insights into its matter distribution and the underlying theory of gravity, and is essential in cosmological analyses for modelling deviations from the Hubble flow. Numerous…