Aiming at the problem that the direct sparse representation of the over-complete dictionary on the image cannot effectively remove the effect of high-frequency noise, and the image reconstruction quality after compressed sensing is not high, an adaptive dictionary learning algorithm based on truncated nuclear norm and low rank decomposition is proposed. The algorithm firstly uses the truncated nuclear norm regularization low-rank decomposition model to decompose the low-rank part and sparse part of the image matrix. The low-rank part retains the main information of the image, and the sparse part mainly contains high-frequency noise and some object contour information. Then, the low-rank part of the image is divided into blocks, and the image blocks are classified according to the texture complexity of the image block. Finally, a K-single value decomposition(K-SVD) dictionary learning algorithm is used to train multiple over-complete dictionaries of different sizes for different categories. Simulation results show that the proposed algorithm can perform better sparse representation of the image, while significantly maintaining the consistency of image block features and significantly improving the quality of image reconstruction.