Anomaly detection is one of the fundamental problems within diverse research areas and application domains. In comparison with most sparse representation based anomaly detection methods adopting a relaxation term of sparsity via 1 norm, we propose an unsupervised anomaly detection method optimized via an adaptive greedy model based on 0 norm constraint, which is more accurate, robust and sparse in theory. Firstly for feature representation, a concise feature space is learned in an unsupervised way via stacked autoencoder network. We propose a dictionary selection model based on 2, 0 norm constraint to select an optimal small subset of the training data to construct a condense dictionary, which can improve accuracy and reduce computational burden simultaneously. Finally, each testing sample is reconstructed by 0 norm constraint based sparse representation, and anomalies are determined depending on the sparse reconstruction scores accordingly. For model optimization, an adaptive forward-backward greedy model is utilized to optimize this nonconvex problem with the theoretical guarantee. Our proposed method is evaluated with our real industrial dataset and benchmark datasets, and various experimental results demonstrate that our proposed method is comparable with conventional supervised methods and performs better than most comparative unsupervised methods.