Karhunen–Loève data imputation in high-contrast imaging

Abstract

The detection and characterization of extended structures is a crucial goal in high-contrast imaging. However, these structures face challenges in data reduction, leading to over-subtraction from speckles and self-subtraction with most existing methods. Iterative post-processing methods offer promising results, but their integration into existing pipelines is hindered by selective algorithms, the high computational cost, and algorithmic regularization. To address this for reference differential imaging (RDI), here we propose a data imputation concept for the Karhunen–Loève transform (DIKL) by modifying two steps in the standard Karhunen–Loève image projection (KLIP) method. Specifically, we partition an image to two matrices: an anchor matrix that focuses only on the speckles to obtain the DIKL coefficients, and a boat matrix that focuses on the regions of astrophysical interest for speckle removal using DIKL components. As an analytical approach, DIKL achieves high-quality results with significantly reduced computational cost (~3 orders of magnitude less than iterative methods). Being a derivative method of KLIP, DIKL is seamlessly integrable into high-contrast imaging pipelines for RDI observations.