Source REconstruction of Arcs behind Cluster Halos ( SourceREACH ): A New Source Reconstruction Algorithm Optimized for Giant Arcs and Galaxy Cluster Lenses

Abstract We introduce a new algorithm designed for reconstructing extended lensed images, specifically giant arcs lensed by galaxy clusters. These highly magnified images contain spatially unique information about both the most uncertain regions of the cluster mass distribution as well as the properties of the background source, but modeling them requires significant computational effort. Our new source reconstruction methodology is designed to be accurate and efficient for high-resolution observations in which point-spread function (PSF) effects are not significant. The overall process deconvolves the observed image by the PSF, delenses the image pixels, and uses interpolation or regression with smoothing to determine the model source. By working with delensed points, the method accounts for varying resolution across the source plane while avoiding the need to construct and manipulate large matrices. We evaluate the speed and accuracy of different interpolation and regression methods using both mock data and real data for the giant arc in Abell 370. We find that utilizing k-nearest neighbors regression results in the best balance of noise smoothing and preservation of compact detail in the source.