Mask based lensless imagers have huge application prospects due to their ultra-thin body. However, the visual perception of the restored images is poor due to the ill conditioned nature of the system. In this work, we proposed a deep analytic network by imitating the traditional optimization process as an end-to-end network. Our network combines analytic updates with a deep denoiser prior to progressively improve lensless image quality over a few iterations. The convergence is proven mathematically and verified in the results. In addition, our method is universal in non-blind restoration. We detailed the solution for the general inverse problem and conducted five groups of deblurring experiments as examples. Both experimental results demonstrate that our method achieves superior performance against the existing state-of-the-art methods.