We present a novel technique estimating the vertical component of particle motion from marine single-component pressure data. The particle motion data, bar an angle-dependent obliquity factor, is computed by convolution of the output from L1 deconvolution of the pressure ghost wavelet with the corresponding ghost wavelet of the particle motion. The estimated particle motion data is then used in a conventional 2D technique for receiver ghost attenuation by combination with the original pressure-wave data. The proposed new technique operates in the τ- domain of individual shot-streamer records and in overlapping windows along the intercept-time axis. In each window, the L1 deconvolution is achieved by an iteratively reweighted-norm least squares algorithm. We applied our technique to deep-tow streamer data of a 3D over/sparse-under marine survey, in which six streamers were towed at a shallow depth, with two additional streamers towed deeper. Over/sparse-under technology allows using seismic measurements from a shallow streamer to be complemented by a low-frequency limited measurement from a deep streamer to achieve an estimate of the up-going pressure wave recording. The low frequencies of the deep streamer are used to boost the low frequencies of the shallow streamer, which have been heavily attenuated by the shallow tow ghost response. Our technique achieves, on this particular data, set improvements in bandwidth of the single-component pressure data, while not fully reaching the quality of the optimally deghosted data from the over/sparse-under survey.