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-Loeve transform (DIKL) by modifying two steps in the standard Karhunen-Loeve 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 focus on the regions of astrophysical interest for speckle removal using DIKL components. As a non-iterative approach, DIKL achieves high-quality results with significantly reduced computational costs (~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.