Phase retrieval plays an important role in vast industrial and scientific applications, which is essentially a non-convex and possible non-smooth optimization problem mathematically. As a special and important case, recovery from Fourier masked measurements is critical for practical imaging including x-ray imaging, material sciences, and optics. In this talk, we mainly concern how to design masks for unique recovery, jointly reconstruct the mask and sample, and design fast convergent splitting algorithm with sparsity modeling.