The linear relationship between the sample complex object wave and its approximated complex Fresnel field obtained using single shot parallel phase-shifting digital holograms (PPSDH) is used in compressive sensing framework and an accurate phase reconstruction is demonstrated. It is shown that the accuracy of phase reconstruction of this method is better than that of compressive sensing adapted single exposure inline holography (SEOL) method. It is derived that the measurement model of PPSDH method retains both the real and imaginary parts of the Fresnel field but with an approximation noise and the measurement model of SEOL retains only the real part exactly equal to the real part of the complex Fresnel field and its imaginary part is completely not available. Numerical simulation is performed for CS adapted PPSDH and CS adapted SEOL and it is demonstrated that the phase reconstruction is accurate for CS adapted PPSDH and can be used for single shot digital holographic reconstruction. © 2018 Society of Photo-Optical Instrumentation Engineers (SPIE).