Spatial sound field interpolation relies on suitable models to 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 of the 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 retains the flexibility of local models to conform to complex sound fields and also preserves the global structure to reconstruct from fewer measurements.