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SUMMARY Long-period underside SS wave reflections have been widely used to furnish global constraints on the presence and depth of mantle discontinuities and to document evidence for their origins, for example, mineral phase-transformations in the transition zone, compositional changes in the mid-mantle and dehydration-induced melting above and below the transition zone. For higher-resolution imaging, it is necessary to separate the signature of the source wavelet (SS arrival) from that of the distortion caused by the mantle reflectivity (SS precursors). Classical solutions to the general deconvolution problem include frequency-domain or time-domain deconvolution. However, these algorithms do not easily generalize when (1) the reflectivity series is of a much shorter period compared to the source wavelet, (2) the bounce point sampling is sparse or (3) the source wavelet is noisy or hard to estimate. To address these problems, we propose a new technique called SHARP-SS: Sparse High-Resolution Algorithm for Reflection Profiling with SS waves. SHARP-SS is a Bayesian deconvolution algorithm that makes minimal a-priori assumptions on the noise model, source signature and reflectivity structure. We test SHARP-SS using real data examples beneath the NoMelt Pacific Ocean region. We recover a low-velocity discontinuity at a depth of $$\sim 69 \pm 4$$ km which marks the base of the oceanic lithosphere, consistent with previous work derived from surface waves, body wave conversions, and ScS reverberations. We anticipate high-resolution fine mantle stratification imaging using SHARP-SS at locations where seismic stations are sparsely distributed.