Phase Recovery Based on the Sparse Measurement

The phase of the signal contains the most information of the object, however, it is very hard to be measured by the conventional optical measuring apparatus directly. The recovery of the missing or irreparably distorted phase, which seeks to reconstruct a complex signal from the amplitude of linear measurements, is of great significance in various fields, particularly in imaging and optics. In recent years, the methods based on convex relaxations and semi-definite programming such as PhaseLift, PhaseCut can recover the phase of signal accurately in over-determined system. This paper focus on the recovery of the phase of sparse measurements based on the PhaseCut algorithm, and proposes a new method called BlockCut by combining the matrix blocking and the PhaseCut algorithm. We extract the equations corresponding to zero-measurement value and solve the obtained homogeneous linear equations, then substitute the results to the rest equations which correspond to non-zero-measurement value and solve it via the PhaseCut algorithm. Experimental results show that the proposed method can improve the accuracy of the original PhaseCut algorithm for the sparse measurements.