The global sparse representation method based on compressed sensing fails to capture the local texture and detail structure of an image. To address this, a local dictionary learning method based on the wavelet domain is proposed. The wavelet high-frequency subband sub-block classification and local dictionary learning are implemented using the FCM clustering method and K-L method, respectively. At the reconstruction end, a compressed sampling Matching pursuit algorithm based on iterative update of sparsity is proposed. This adaptive iteration can effectively reconstruct the original image under unknown sparsity conditions. Simulation experiments show that compared to existing reconstruction methods, this approach has the advantages of simple computation, strong adaptive sparse representation ability for the original image, and superior reconstructed image performance.