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Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a…
The numerical flow iteration method has recently been proposed as a memory-slim solution method for the Vlasov--Poisson system. It stores the temporal evolution of the electric field and reconstructs the solution in each time step by…
Although diffusion-based real-world image restoration (Real-IR) has achieved remarkable progress, efficiently leveraging ultra-large-scale pre-trained text-to-image (T2I) models and fully exploiting their potential remain significant…
Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…
The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics)…
Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive…
The Frank-Wolfe (FW) method, which implements efficient linear oracles that minimize linear approximations of the objective function over a fixed compact convex set, has recently received much attention in the optimization and machine…
In this paper we study the problem of recovering a low-rank matrix from linear measurements. Our algorithm, which we call Procrustes Flow, starts from an initial estimate obtained by a thresholding scheme followed by gradient descent on a…
In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then…
The three-dimensional Time-Resolved Lagrangian Particle Tracking (3D TR-LPT) technique has recently advanced flow diagnostics by providing high spatiotemporal resolution measurements under the Lagrangian framework. To fully exploit its…
This paper discusses the noisy phase retrieval problem: recovering a complex image signal with independent noise from quadratic measurements. Inspired by the dark fringes shown in the measured images of the array detector, a novel phase…
In subsurface multiphase flow simulations, poor nonlinear solver performance is a significant runtime sink. The system of fully implicit mass balance equations is highly nonlinear and often difficult to solve for the nonlinear solver,…
Phase retrieval (PR) is a crucial problem in many imaging applications. This study focuses on resolving the holographic phase retrieval problem in situations where the measurements are affected by a combination of Poisson and Gaussian…
In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…
Wavefront phase retrieval from a set of intensity measurements can be formulated as an optimization problem. Two nonconvex objective models (MLP and its variants LS) based on maximum likelihood estimation are investigated. We develop…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…
Phase retrieval refers to the problem of recovering a high-dimensional vector $\boldsymbol{x} \in \mathbb{C}^N$ from the magnitude of its linear transform $\boldsymbol{z} = A \boldsymbol{x}$, observed through a noisy channel. To improve the…
Purpose: To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging. Theory and Methods: The problem of enforcing phase constraints in reconstruction…