Sparsity promoting automatic focusing in digital holography

Sparsity properties of digital holograms have been investigated for application in compressive holography, permitting the discovery of the sparsest reconstruction plane in which the recovery of digital holograms is suitable. Recent approaches for denoising and phase retrieval are also proposed exploiting the sparsity properties of digital holograms. Thus it can be shown a strong correlation between holograms sparsity and focal plane detection, making a sparsity measure coefficient as a candidate to be used for focus plane calculation. Here we implement different sparsity metrics, that are able to measure a degree of sparsity of reconstructed digital hologram and we investigate their relation with the automatic focusing criterions, highlighting the possibility to use a sparsity measure as refocusing metric as well as the contrary, i.e. using image contrast coefficients as sparsity measures. Our analysis will be reported for digital holograms recorded in both lensless and microscope configuration and for both amplitude and pure-phase objects.