相关论文: Optimal Spectral Initialization for Signal Recover…
We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic…
Optical spectrometers have propelled scientific and technological advancements in a wide range of fields. While sophisticated systems with excellent performance metrics are serving well in controlled laboratory environments, many…
In recent literature, a general two step procedure has been formulated for solving the problem of phase retrieval. First, a spectral technique is used to obtain a constant-error initial estimate, following which, the estimate is refined to…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered…
Our focus is on robust recovery algorithms in statistical linear inverse problem. We consider two recovery routines - the much studied linear estimate originating from Kuks and Olman [42] and polyhedral estimate introduced in [37]. It was…
A novel phase retrieval algorithm for broadband hyperspectral phase imaging from noisy intensity observations is proposed. It utilizes advantages of the Fourier Transform spectroscopy in the self-referencing optical setup and provides,…
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples…
We revisit a stochastic control problem of optimally modifying the underlying spectrally negative Levy process. A strategy must be absolutely continuous with respect to the Lebesgue measure, and the objective is to minimize the total costs…
Spectral methods are widely used in geometry processing of 3D models. They rely on the projection of the mesh geometry on the basis defined by the eigenvectors of the graph Laplacian operator, becoming computationally prohibitive as the…
This paper presents two inexact composite gradient methods, one inner accelerated and another doubly accelerated, for solving a class of nonconvex spectral composite optimization problems. More specifically, the objective function for these…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used…
In this paper, we consider the optimal design of photonic crystal band structures for two-dimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue…
We develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems.…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
Optimal design of a Phase I cancer trial can be formulated as a stochastic optimization problem. By making use of recent advances in approximate dynamic programming to tackle the problem, we develop an approximation of the Bayesian optimal…
We describe a "spatio-spectral" deconvolution algorithm for wide-band imaging in radio interferometry. In contrast with the existing multi-frequency reconstruction algorithms, the proposed method does not rely on a model of the…