Today we have a more in-depth look at interferometry using a sphere as a support and its connection to Compressive Sensing in Compressed sensing for wide-field radio interferometric imaging by Jason D. McEwen, Yves Wiaux. The abstract reads:
For the next generation of radio interferometric telescopes it is of paramount importance to incorporate wide field-of-view (WFOV) considerations in interferometric imaging, otherwise the fidelity of reconstructed images will suffer greatly. We extend compressed sensing techniques for interferometric imaging to a WFOV and recover images in the spherical coordinate space in which they naturally live, eliminating any distorting projection. The effectiveness of the spread spectrum phenomenon, highlighted recently by one of the authors, is enhanced when going to a WFOV, while sparsity is promoted by recovering images directly on the sphere. Both of these properties act to improve the quality of reconstructed interferometric images. We quantify the performance of compressed sensing reconstruction techniques through simulations, highlighting the superior reconstruction quality achieved by recovering interferometric images directly on the sphere rather than the plane.
I note from their conclusion:
...Extensions to realistic and continuous visibility coverage and their impact on compressed sensing based interferometric imaging are now of considerable importance. In general, compressed sensing addresses imaging by optimising both reconstruction and acquisition, while we have essentially focused on reconstruction only. The possibility of optimising the configuration of interferometers to enhance the spread spectrum phenomenon for compressed sensing reconstruction is an exciting avenue of research at the level of acquisition. In addition, direction dependent beam e ects may also provide an alternative source of the spread spectrum phenomenon...