  Spatial sound field interpolation relies on suitable models to both conform
to available measurements and predict the sound field in the domain of
interest. A suitable model can be difficult to determine when the spatial
domain of interest is large compared to the wavelength or when spherical and
planar wavefronts are present or the sound field is complex, as in the
near-field. To span such complex sound fields, the global reconstruction task
can be partitioned into local subdomain problems. Previous studies have shown
that partitioning approaches rely on sufficient measurements within each
domain, due to the higher number of model coefficients. This study proposes a
joint analysis of all local subdomains, while enforcing self-similarity between
neighbouring partitions. More specifically, the coefficients of local plane
wave representations are sought to have spatially smooth magnitudes. A
convolutional model of the sound field in terms of plane wave filters is
formulated and the inverse reconstruction problem is solved via the alternating
direction method of multipliers. The experiments on simulated and measured
sound fields suggest, that the proposed method both retains the flexibility of
local models to conform to complex sound fields and also preserves the global
structure to reconstruct from fewer measurements.
