Abstract: The compressive sensing based digital watermarking algorithm solves the sparse coefficients by using the random measurement matrix at the detection port,but such operation usually results in time-consuming detection process,lacks of practicality and the quality of the watermark reconstructed by compressive sensing is generally low.To address these issues,a novel watermarking algorithms using the sparse transform and Laplacian pyramid is proposed.Our formulations combine a new sparse model(i.e.,sparse transform),decompose the carrier image using the single-layer Laplacian pyramid at the embedding port,and segment the low frequency subband uniformly.Then,the segmented image patches are expanded into vectors to learn the sparse transform,and choose the minimum value of the global coefficients in the sparse domain for embedding.As a result,when detecting the watermark,one can adopt the matrix multiplication strategy directly to transform the low-frequency subband of the watermarked images into the sparse domain for detection,which can avoid the process of re-calculating the sparse coefficients.Extensive experiments demonstrate that our proposed method can cost less time for detection,has better transparency,and moreover is robust against attacking images,such as JPEG compression,filtering,noise and cutting.