Unsupervised anomaly localization, which plays a critical role in industrial manufacturing, is to identify anomalous regions that deviate from patterns established exclusively from nominal samples. Recent mainstream methods focus on approximating the target feature distribution by leveraging embeddings from ImageNet models. However, a common issue in many anomaly localization methods is the lack of adaptability of the feature approximations to specific targets. Consequently, their ability to effectively identify anomalous regions relies significantly on the data coverage provided by the finite resources in a memory bank. In this paper, we propose a novel subspace-aware feature reconstruction framework for anomaly localization. To achieve adaptive feature approximation, our proposed method involves the reconstruction of the feature representation through the self-expressive model designed to learn low-dimensional subspaces. Importantly, the sparsity of the subspace representation contributes to covering feature patterns from the same subspace with fewer resources, leading to a reduction in the memory bank. Extensive experiments across three industrial benchmark datasets demonstrate that our approach achieves competitive anomaly localization performance compared to state-of-the-art methods by adaptively reconstructing target features with a small number of samples.