1. A method for denoising input seismic data d, the method comprising: receiving the input seismic data d recorded in a first domain by seismic receivers, wherein the input seismic data d includes pure seismic data ss relating to an exploration source and coherent noise data n generated by a man-made device; generating a model m in a second domain to describe the input seismic data d; and processing the model m to obtain an output seismic dataset d′ indicative of seismic data substantially free of the coherent noise data n generated by the man-made device.