Abstract: A Time domain Compressive Synthetic Aperture Sonar imaging method(TC-SAS) for underwater sparse targets is proposed,which achieves high-resolution real-time imaging of underwater acoustic targets.Through the aperture synthesis of multiple subarrays,the Green's function from the imaging grid point to the frame by frame array within the effective aperture is constructed in the time domain,and the mapping matrix from the scattering intensity of the imaging area to the data domain is given.Then,using the prior knowledge of spatial sparsity of the area,the scattering coefficient matrix of the imaging area is obtained by the sparse reconstruction method of orthogonal matching pursuit,and the sparse target high-resolution imaging is realized.At the same time,a data reduction method is proposed for Linear Frequency Modulation(LFM) signal,which reduces the data scale by intercepting the observation data and dictionary matrix after pulse compression at the same time;furthermore,combining with the method of looking up the two-dimensional matrix table,the real-time imaging of the block is realized by exchanging space for time.Numerical simulation and lake experiments show that the proposed algorithm can distinguish the target which is difficult to be distinguished by the traditional time delay summation algorithm,and the image clarity index is improved by 4.9 dB on average,which improves the imaging quality of synthetic aperture sonar.