Most of the information of optical wavefront is encoded in the phase which includes more details of the object.
Conventional optical measuring apparatus is relatively easy to record the intensity of light, but can not measure the phase
of light directly. Thus it is important to recovery the phase from the intensity measurements of the object. In recent years,
the methods based on quadratic programming such as PhaseLift and PhaseCut can recover the phase of general signal
exactly for overdetermined system. To retrieve the phase of sparse signal, the Compressive Phase Retrieval (CPR)
algorithm combines the l1-minimization in Compressive Sensing (CS) with low-rank matrix completion problem in
PhaseLift, but the result is unsatisfied. This paper focus on the recovery of the phase of sparse signal and propose a new
method called the Compressive Phase Cut Retrieval (CPCR) by combining the CPR algorithm with the PhaseCut
algorithm. To ensure the sparsity of the recovered signal, we use CPR method to solve a semi-definite programming
problem firstly. Then apply linear transformation to the recovered signal, and set the phase of the result as the initial
value of the PhaseCut problem. We use TFOCS (a library of Matlab-files) to implement the proposed CPCR algorithm in
order to improve the recovered results of the CPR algorithm. Experimental results show that the proposed method can
improve the accuracy of the CPR algorithm, and overcome the shortcoming of the PhaseCut method that it can not
recover the sparse signal effectively.