Adaptive Semi-linear Inversion of Strong Gravitational Lens Imaging

TL;DR

This paper introduces an adaptive pixelization method for gravitational lens inversion that improves reliability and efficiency by customizing source plane pixelization to lens magnification, reducing biases and systematics.

Contribution

The paper presents a novel adaptive semi-linear inversion technique using h-means clustering for source pixelization, enhancing modeling accuracy over fixed grid methods.

Findings

Adaptive SLI outperforms standard SLI in modeling singular power law ellipsoid lenses.

The method reliably samples complex posterior distributions with a single non-linear search.

Adaptive SLI reduces biases and systematics in lens modeling.

Abstract

We present a new pixelized method for the inversion of gravitationally lensed extended source images which we term adaptive semi-linear inversion (SLI). At the heart of the method is an h-means clustering algorithm which is used to derive a source plane pixelization that adapts to the lens model magnification. The distinguishing feature of adaptive SLI is that every pixelization is derived from a random initialization, ensuring that data discretization is performed in a completely different and unique way for every lens model parameter set. We compare standard SLI on a fixed source pixel grid with the new method and demonstrate the shortcomings of the former when modeling singular power law ellipsoid (SPLE) lens profiles. In particular, we demonstrate the superior reliability and efficiency of adaptive SLI which, by design, fixes the number of degrees of freedom (NDOF) of the optimization and thereby removes biases present with other methods that allow the NDOF to vary. In addition, we highlight the importance of data discretization in pixel-based inversion methods, showing that adaptive SLI averages over significant systematics that are present when a fixed source pixel grid is used. In the case of the SPLE lens profile, we show how the method successfully samples its highly degenerate posterior probability distribution function with a single non-linear search. The robustness of adaptive SLI provides a firm foundation for the development of a strong lens modeling pipeline, which will become necessary in the short-term future to cope with the increasing rate of discovery of new strong lens systems.