Penalized least-squares for imaging with hypertelescopes.

Area of Science:

• Astronomy and Astrophysics
• Optical Engineering

Background:

• Conventional telescopes are limited by aperture size and atmospheric turbulence.
• Sparse aperture telescopes (SATs) use multiple small apertures for improved angular resolution.
• Densified hypertelescopes enable direct image formation from large SATs.

Purpose of the Study:

• To evaluate a penalized least-squares (PLS) object-estimation approach for hypertelescope image reconstruction.
• To compare the PLS method with the Richardson-Lucy (RL) deconvolution algorithm.
• To optimize PLS parameters for high-fidelity image reconstruction.

Main Methods:

• Implementation of a PLS object-estimation algorithm for sparse aperture imaging.
• Application of the RL deconvolution algorithm to hypertelescope data.
• Parameter optimization for PLS using structure similarity metrics in simulations.

Main Results:

• The PLS approach significantly improves image reconstruction fidelity.
• Optimized PLS parameters yield superior results compared to RL.
• Densification in hypertelescopes suppresses side lobes but introduces unique point-spread function structures.

Conclusions:

• PLS is a powerful technique for reconstructing images from sparse aperture arrays.
• The PLS method offers a substantial advantage over classical RL for hypertelescope imaging.
• Further research can refine PLS for advanced astronomical imaging applications.