arXiv subjects

Isaac Viviano

Publications and source records attributed to Isaac Viviano.

3 recordsLinked to original sources

arXiv2026

Recovery of Integer Signals from Limited DFT Samples: Lattice Methods and Stability Analysis

We analyze lattice-based algorithms for recovering integer-valued signals from partial discrete Fourier transform (DFT) measurements. These algorithms formulate signal recovery as the problem of finding short vectors in an appropriately constructed lattice. We derive parameter estimates that guarantee successful recovery and quantify how these estimates depend on the signal length, the error of an initial guess, and the number of sampled DFT coefficients. The analysis characterizes the stability of the inversion algorithms, as the lattice parameters are closely related to the required measurement precision. Numerical experiments demonstrate close agreement between the theoretical predictions and observed recovery thresholds over a broad range of problem parameters.

math.NA↗

arXiv2026

Recovery of Integer Images from Minimal DFT Measurements: Uniqueness and Inversion Algorithms

Exact reconstruction of an image from measurements of its Discrete Fourier Transform (DFT) typically requires all DFT coefficients to be available. However, incorporating the prior assumption that the image contains only integer values enables unique recovery from a limited subset of DFT coefficients. This paper develops both theoretical and algorithmic foundations for this problem. We use algebraic properties of the DFT to define a reduction from two-dimensional recovery to several well-chosen one-dimensional recoveries. Our reduction framework characterizes the minimum number and location of DFT coefficients that must be sampled to guarantee unique reconstruction of an integer-valued image. Algorithmically, we develop reconstruction procedures which use dynamic programming to efficiently recover an integer signal or image from its minimal set of DFT measurements. While the new inversion algorithms still involve NP-hard subproblems, we demonstrate how the divide-and-conquer approach drastically reduces the associated search space. To solve the NP-hard subproblems, we employ a lattice-based framework which leverages the LLL approximation algorithm to make the algorithms fast and practical.

math.NA↗

arXiv2026

Estimation of a Gas Diffusion Coefficient by Fitting Molecular Dynamics Trajectories to Finite-Difference Simulations

A procedure is presented to estimate the diffusion coefficient of a uniform patch of argon gas in a uniform background of helium gas. Molecular Dynamics (MD) simulations of the two gases interacting through the Lennard-Jones potential are carried out using the LAMMPS software package. In addition, finite-difference (FD) calculations are used to solve the continuum diffusion equation for the argon concentration with a given diffusion coefficient. To contain the computational cost and facilitate data visualization, both MD and FD computations were done in two space dimensions. The MD argon trajectories were binned to the FD grid, and the optimal diffusion coefficient was estimated by minimizing the difference between the binned MD data and the FD solution with a nonlinear least squares procedure (Levenberg-Marquardt algorithm). Numerical results show the effect of the MD binning parameter and FD grid spacing. The estimated diffusion coefficient is compared to an experimental measurement.

math.NA↗