Computing device, computer instructions and method for improving accuracy of an image of a surveyed subsurface. The method includes a step of receiving seismic data (D) recorded with seismic sensors; a step of deghosting the seismic data (D) using a sparseT-Pinversion algorithm together with a low-rank optimization scheme and a high-cut filter to calculate ghost-free wave-fields (U0(t,x,y)) in the time-space domain; and a step of processing the ghost-free wave-fields (U0(t,x,y)) to generate the image of the surveyed subsurface.