Core Concepts
Focusing on gradient descent methods for low-dose Poisson phase retrieval.
Abstract
The content discusses Wirtinger gradient descent methods for low-dose Poisson phase retrieval. It covers the problem of phase retrieval in optical imaging, focusing on low-dose illumination with Poisson noise. The article explores gradient descent algorithms, regularizations, and approximations for this specific scenario. It delves into the convergence of gradient descent algorithms, numerical experiments, and variance stabilization methods for Gaussian log-likelihood losses. Theoretical analysis and practical experiments are presented to validate the effectiveness of the proposed methods.
Stats
Numerical experiments are based on a test object x ∈Cn with n = 256.
Gaussian measurement vectors ai ∈Cn, i = 1, . . . , m, where m = 10n.
Doses range from 500 to 4000 with corresponding signal-to-noise ratios.
Regularization parameters ε used in the Poisson flow algorithm: 10^-3, 0.1, 0.25, 0.5, 1.
Variance stabilization parameters c1 = 0.12, c2 = 0.27 for optimized variance-stabilizing transforms.
Quotes
"The problem of phase retrieval has many applications in the field of optical imaging."
"In all practical relevant measurement scenarios, the data yi is corrupted by some sort of noise."
"The algorithm using the suggested loss function with the optimized variance-stabilizing transform performs comparably to the Poisson flow."