With the widespread use of hyperspectral images, hyperspectral image technology has made considerable progress, of which hyperspectral image anomaly detection technology has received more and more attention. In order to solve the problem of poor practicability and poor detection effect of traditional hyperspectral image anomaly detection techniques, this paper presents a novel low rank representation detection algorithm. For hyperspectral images, most of the background pixels can be approximated by a small number of major background pixel combinations, and their representation coefficients will be located in a low-rank space. While the remaining anomalous pixels in the sparse part that can not be represented by the main background pixels can be extracted by the detection algorithm. In low-rank representations, the construction of the background pixel dictionary will affect the representation of the background pixels in the hyperspectral image. When extracting the background pixels directly from the existing hyperspectral image to construct the dictionary, this process will lead to the contamination of the background pixel dictionary by the abnormal pixels. So in this paper, the background pixel dictionary is constructed by using the observed data on the hyperspectral image to be detected and the potential unobserved data that can be synthesized by the principle of spectral composition, and the main features of the background pixels are extracted, helping to better separate the sparse anomalous pixel Information. Hyperspectral image data is characterized by high-dimensional geometry. In this paper, we introduce a Laplacian matrix to constrain the representation of locally similar pixels in the space to be detected, and get a closer representation of the true representation coefficients. The experimental results are validated respectively on the simulation data and the real data, showing that the proposed method reduces the false detection rate by effectively highlighting the abnormal pixels and improves the detection rate by suppressing the background pixels.