Sparsity averaging for radio-interferometric imaging

We propose a novel regularization method for compressive imaging in the context of the compressed sensing (CS) theory with coherent and redundant dictionaries. Natural images are often complicated and several types of structures can be present at once. It is well known that piecewise smooth images exhibit gradient sparsity, and that images with extended structures are better encapsulated in wavelet frames. Therefore, we here conjecture that promoting average sparsity or compressibility over multiple frames rather than single frames is an extremely powerful regularization prior.

💡 Research Summary

The paper introduces a novel regularization strategy for compressive imaging, specifically tailored to radio‑interferometric (RI) reconstruction, by exploiting “average sparsity” across multiple coherent dictionaries. Instead of assuming that an image is sparse in a single basis, the authors concatenate q frames— the Dirac (pixel) basis and the first eight orthonormal Daubechies wavelet bases (Db1‑Db8)—into a single analysis operator Ψ = (1/√q)