Global Optimization methods for Gravitational Lens Systems with Regularized Sources

TL;DR

This paper introduces a novel two-stage global optimization approach using genetic algorithms and regularization techniques to accurately model gravitational lens systems, validated on SLACS survey data.

Contribution

It combines analytical and pixelated source modeling with regularization and model selection criteria, advancing gravitational lens modeling methods.

Findings

Effective estimation of source degrees of freedom.

Successful application to SLACS survey systems.

Justification of regularization parameter selection.

Abstract

Several approaches exist to model gravitational lens systems. In this study, we apply global optimization methods to find the optimal set of lens parameters using a genetic algorithm. We treat the full optimization procedure as a two-step process: an analytical description of the source plane intensity distribution is used to find an initial approximation to the optimal lens parameters. The second stage of the optimization uses a pixelated source plane with the semilinear method to determine an optimal source. Regularization is handled by means of an iterative method and the generalized cross validation (GCV) and unbiased predictive risk estimator (UPRE) functions that are commonly used in standard image deconvolution problems. This approach simultaneously estimates the optimal regularization parameter and the number of degrees of freedom in the source. Using the GCV and UPRE functions we are able to justify an estimation of the number of source degrees of freedom found in previous work. We test our approach by applying our code to a subset of the lens systems included in the SLACS survey.