Abstract: Deep Convolutional Neural Networks (CNNs)-based methods have achieved significant breakthroughs in the task of single image shadow removal. However, the performance of these methods remains limited for several reasons. First, the existing shadow illumination model ignores the spatially-variant property of the shadow images, hindering their further performance. Second, most deep CNNs-based methods directly estimate the shadow-free results from the input shadow images like a black box, thus losing the desired interpretability. To address these issues, we first propose a new shadow illumination model for the shadow removal task. This new shadow illumination model ensures the identity mapping among non-shadow regions, and adaptively performs fine-grained spatial mapping between shadow regions and their references. Then, based on the shadow illumination model, we reformulate the shadow removal task as a variational optimization problem. To effectively solve the variational problem, we design an iterative algorithm and unfold it into a deep network, naturally increasing the interpretability of the deep model. Experiments show that our method could achieve state-of-the-art performance with 46% parameters, 21% floating point of operations (FLOPs) and over 17 times faster than SOTA method DHAN \cite{cun2020towards}.