SUPPOSe: A deconvolution method for low dimensionality images.

SANDRA MARTINEZ

Encuentro; The annual Rose in Science Event (RISE); 2022

Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP)

The question of how to extract all the information contained in an image that is blurred by the convolution of the object with the instrumental response (PSF) it is a problem always encountered in every measurement. It is well known that straightforward deconvolution is an ill posed problem, that means that there is loss of information but also the retrieval can lead to unstable results that cannot be circumvented by computational power. In the last years that problem has been overcome in the cases where we can assume some additional hypothesis over the retrieval object. Some of them are the assumption that there is only one molecule per deconvolution (single molecule localization methods (SMLM)), or that the original object is sparse (like in compressed sensing methods).Recently, we have developed the method SUPPOSe (from SUPerposition of POint Sources) where we assume that the solution can be well approximated by expressing it as a sum of sources of the same intensity. This is the additional information added that circumvents the instability of the solutions and the loss of information in the convolution. I will present the method and show how the number of virtual sources can be estimated and depends among other terms, on the number of real sources. I will show how this parameter acts as a regularization term. Again, a restrictions appear and the method works for images of low dimensionality as typically found in intracellular structures with filiform or sparse shapes. Some experimental results will be presented too.