Computing device, computer instructions and method for simultaneously denoizing and attenuating multiples in seismic data recorded with seismic receivers. The method includes receiving the seismic data, wherein the seismic data includes a pressure P component and a vertical Z component; separating the seismic data into up-going U wave-fields and down-going D wave-fields; calculating an up-down deconvolution R based on the up-going U and the down-going D wave-fields; generating a multiple model M based on the up-down deconvolution R; and adaptively subtracting the multiple model M from the pressure P component to obtain a corrected pressure Pfree component from which simultaneously the noise and the multiples were removed. A multiple is a wave-field that propagates from a source to a receiver and experiences more than one reflection.