Visual anomaly detection is an essential component in modern industrial manufacturing. Existing studies using notions of pairwise similarity distance between a test feature and nominal features have achieved great breakthroughs. However, the absolute similarity distance lacks certain generalizations, making it challenging to extend the comparison beyond the available samples. This limitation could potentially hamper anomaly detection performance in scenarios with limited samples. This article presents a novel sparse feature representation anomaly detection (SFRAD) framework, which formulates the anomaly detection as a sparse feature representation problem; and notably proposes an anomaly score by orthogonal matching pursuit (ASOMP) as a novel detection metric. Specifically, SFRAD calculates the Gaussian kernel distance between the test feature and its sparse representation in the nominal feature space for anomaly detection. Here, the orthogonal matching pursuit (OMP) algorithm is adopted to achieve the sparse feature representation. Moreover, to construct a low-redundancy memory bank storing the basis features for sparse representation, a novel basis feature sampling (BFS) algorithm is proposed by considering both the maximum coverage and the optimum feature representation simultaneously. As a result, SFRAD incorporates both the advantages of absolute similarity and linear representation; and this enhances the generalization in low-shot scenarios. Extensive experiments on the MVTec anomaly detection (MVTec AD), Kolektor surface-defect dataset (KolektorSDD), Kolektor surface-defect dataset 2 (KolektorSDD2), MVTec logical constraints anomaly detection (MVTec LOCO AD), Visual anomaly (VISA), Modified national institute of standards and technology (MNIST), and CIFAR-10 datasets demonstrate that our proposed SFRAD outperforms the previous methods and achieves state-of-the-art unsupervised anomaly detection performance. Notably, significantly improved outcomes and results have also been achieved on low-shot anomaly detection. Code is available at https//github.com/fanghuisky/SFRAD.