Richard Y. Chen
California Institute of Technology
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Publication
Featured researches published by Richard Y. Chen.
Annals of Probability | 2014
Lester W. Mackey; Michael I. Jordan; Richard Y. Chen; Brendan Farrell; Joel A. Tropp
This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein’s method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix generalizations of the classical inequalities due to Hoeffding, Bernstein, Khintchine and Rosenthal. The same technique delivers bounds for sums of dependent random matrices and more general matrix-valued functions of dependent random variables.
New Journal of Physics | 2015
Roarke Horstmeyer; Richard Y. Chen; Xiaoze Ou; Brendan P. W. Ames; Joel A. Tropp; Changhuei Yang
Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that currently solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the ptychographic reconstruction algorithm that is currently in widespread use.
Optics Express | 2012
Roarke Horstmeyer; Richard Y. Chen; Benjamin Judkewitz; Changhuei Yang
Optical speckle is commonly observed in measurements using coherent radiation. While lacking experimental validation, previous work has often assumed that speckles random spatial pattern follows a Markov process. Here, we present a derivation and experimental confirmation of conditions under which this assumption holds true. We demonstrate that a detected speckle field can be designed to obey the first-order Markov property by using a Cauchy attenuation mask to modulate scattered light. Creating Markov speckle enables the development of more accurate and efficient image post-processing algorithms, with applications including improved de-noising, segmentation and super-resolution. To show its versatility, we use the Cauchy mask to maximize the entropy of a detected speckle field with fixed average speckle size, allowing cryptographic applications to extract a maximum number of useful random bits from speckle images.
arXiv: Probability | 2012
Richard Y. Chen; Alex Gittens; Joel A. Tropp
Electronic Journal of Probability | 2014
Joel A. Tropp; Richard Y. Chen
arXiv: Computer Vision and Pattern Recognition | 2017
Roarke Horstmeyer; Richard Y. Chen; Barbara Kappes; Benjamin Judkewitz
arXiv: Computer Vision and Pattern Recognition | 2016
Richard Y. Chen; Yating Jing; Hunter Jackson
Archive | 2012
Richard Y. Chen; Alex Gittens; Joel A. Tropp
arXiv: Computer Vision and Pattern Recognition | 2018
Richard Y. Chen; Faisal Mahmood; Alan L. Yuille; Nicholas J. Durr
arXiv: Computer Vision and Pattern Recognition | 2018
Faisal Mahmood; Daniel Borders; Richard Y. Chen; Gregory N. McKay; Kevan J. Salimian; Alexander Baras; Nicholas J. Durr