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The reconstruction of multipolar acoustic or electromagnetic sources fromtheir far-field signature plays a crucial role in numerous applications. Mostof the existing techniques require dense multi-frequency data at the Nyquistsampling rate. The availability of a sub-sampled grid contributes to the nullspace of the inverse source-to-data operator, which causes significant imagingartifacts. For this purpose, additional knowledge about the source orregularization is required. In this letter, we propose a novel two-stagestrategy for multipolar source reconstruction from sub-sampled sparse data thattakes advantage of the sparsity of the sources in the physical domain. The dataat the Nyquist sampling rate is recovered from sub-sampled data and then aconventional inversion algorithm is used to reconstruct sources. The datarecovery problem is linked to a spectrum recovery problem for the signal withthe \textit{finite rate of innovations} (FIR) that is solved using anannihilating filter-based structured Hankel matrix completion approach (ALOHA).For an accurate reconstruction, a Fourier inversion algorithm is used. Thesuitability of the approach is supported by experiments.

Multipolar Acoustic Source Reconstruction from Sparse Far-Field Data using ALOHA