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, high computational cost, and algorithmic regularization. To address this for reference differential imaging (RDI), here we propose the data imputation concept to Karhunen-Lo\`eve transform (DIKL) by modifying two steps in the standard Karhunen-Lo\`eve image projection (KLIP) method. Specifically, we partition an image to two matrices: an anchor matrix which focuses only on the speckles to obtain the DIKL coefficients, and a boat matrix which 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.

翻译：探测并表征延展结构是高反差成像领域的关键目标。然而，此类结构在数据处理中面临挑战：多数现有方法会导致散斑过度减除与自减除问题。迭代后处理方法虽展现出良好前景，但其受限于选择性算法、高计算成本及算法正则化，难以整合至现有处理流程。为解决参考差分成像（RDI）中的上述难题，本文提出将数据插补概念引入Karhunen-Loève变换（DIKL），通过改进标准Karhunen-Loève图像投影（KLIP）方法中的两个步骤实现。具体而言，我们将图像划分为两个矩阵：锚定矩阵仅聚焦散斑以获取DIKL系数，而载体矩阵则聚焦天体物理目标区域，利用DIKL分量进行散斑去除。作为一种解析方法，DIKL能以极低计算成本（较迭代方法降低约三个数量级）获得高质量结果。作为KLIP的衍生方法，DIKL可无缝集成于RDI观测的高反差成像处理流程中。