In order to recover wrapped phase map with the noisy and under-sampled area rapidly and accurately, the algorithms of fast Fourier transform (FFT)-based method of least squares (FFT-LS), discrete cosine transform (DCT)-based method of least squares (DCT-LS), lateral shearing based method of least squares (LS-LS) and the algorithm of preconditioned conjugate gradient (PCG) method are compared through theoretical analysis, computer simulation and experimental verification. The results show that the algorithm of DCT-LS is the fastest, the algorithm of LS-LS is second to DCT-LS, and the algorithm of PCG is the slowest. For strong noise, the algorithm of PCG has the best effect, and the algorithm of LS-LS has the best effect for dealing with under-sampling.