Due to environmental and economic constraints inherent to seismic exploration, there are often missing shotpoints and receivers that degrade the resolution of the final seismic image. Hence sophisticated interpolation techniques are required for the recovery of dense and uniform spatial sampling. Recent approaches improve the interpolation by adopting robust models through denoisers. We introduce a 3D shot gather interpolation method that jointly considers a sparse prior and a regularization induced by a multichannel volumetric denoiser. The proposed volumetric regularization uses collaborative filters that perform denoising through transform-domain shrinkage of a group of similar seismic cubes extracted from a land seismic acquisition. This grouping and collaborative filtering paradigm exploit the local correlation present in each cube and the non-local correlation between different cubes. Experiments on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Stratton 3D survey</i> show that the proposed method can interpolate 3D shot gathers in an orthogonal seismic recording from a swath geometry, outperforming methods based on 2D denoisers and 5D seismic data reconstruction in terms of root mean square error and in the recovery of seismic reflections.