Related papers: Proximity Operators for Phase Retrieval

This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental…

In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…

This paper investigates a recursive formulation of auto-regressive multi-fidelity Gaussian process regression in the challenging setting of noisy and non-nested high- and low-fidelity data. We propose a decoupled optimization strategy based…

In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…

We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of randomly selected resolvents of monotone operators and,…

Noise poses a challenge for learning dynamical-system models because already small variations can distort the dynamics described by trajectory data. This work builds on operator inference from scientific machine learning to infer…

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…

Advances in compressive sensing provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with…

A gradient recovery operator based on projecting the discrete gradient onto the standard finite element space is considered. We use an oblique projection, where the test and trial spaces are different, and the bases of these two spaces form…

Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…

This paper focuses on random projection operators when the subspace of projection is estimated. We derive non-asymptotic upper bounds on the error between the projection onto the estimated subspace and the projection onto the underlying…

This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic $O(1/n)$ convergence rate of our proposed algorithm in…

In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one must perform a process known as phase retrieval. This paper…

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy,…

Projection-based integrators are effectively employed in high-precision systems with growing industrial success. By utilizing a projection operator, the resulting projection-based integrator keeps its input-output pair within a designated…

Many numerical algorithms have been established to reconstruct pressure fields from measured kinematic data with noise by Particle Image Velocimetry (PIV), such as the Pressure Poisson solver and the Omni-Directional Integration (ODI)…

We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

Traditional frequency based projection filters, or projection operators (PO), separate signal and noise through a series of transformations which remove frequencies where noise is present. However, this technique relies on a priori…

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…