Related papers: A tomographic approach to non-Markovian master equ…
In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed in [3] where an automated parameter selection rule for…
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
We consider an inverse boundary value problem for a model time-harmonic equation of acoustic tomography of moving fluid with variable current velocity, sound speed, density and absorption. In the present article it is assumed that at fixed…
A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is…
We present a novel approach for fully non-stationary Gaussian process regression (GPR), where all three key parameters -- noise variance, signal variance and lengthscale -- can be simultaneously input-dependent. We develop gradient-based…
By extending to the stochastic setting the classical vanishing viscosity approach we prove the existence of suitably weak solutions of a class of nonlinear stochastic evolution equation of rate-independent type. Approximate solutions are…
In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…
We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…
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…
We study a classical reparametrization-invariant system, in which ``time'' is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a…
This paper presents a new Bayesian model and algorithm for nonlinear unmixing of hyperspectral images. The model proposed represents the pixel reflectances as linear combinations of the endmembers, corrupted by nonlinear (with respect to…
Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…
Complex systems display variability over a broad range of spatial and temporal scales. Some scales are unresolved due to computational limitations. The impact of these unresolved scales on the resolved scales needs to be parameterized or…
Ptychography, a prevalent imaging technique in fields such as biology and optics, poses substantial challenges in its reconstruction process, characterized by nonconvexity and large-scale requirements. This paper presents a novel approach…
We investigate time encoding as an alternative method to classical sampling, and address the problem of reconstructing classes of non-bandlimited signals from time-based samples. We consider a sampling mechanism based on first filtering the…
A generalization of the stochastic wave function method to quantum master equations which are not in Lindblad form is developed. The proposed stochastic unravelling is based on a description of the reduced system in a doubled Hilbert space…
Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent…