**Speaker: Emmanuel Soubies**

**Abstract:** In this talk, we present a novel statistical dictionary learning algorithm based on an alpha-stable innovation model [1]. The main idea of the method relies on the property that knowing the marginal dispersions of symmetric alpha stable (SaS) random vectors is equivalent to knowing the Radon transform of their PDFs. Hence, considering a signal model y=Ax where x is an unknown SaS random vector, A is a dictionary matrix and y is an observation vector, it turns out that A is identifiable from an appropriate set of data projections. The identification is performed by minimizing a new cost function by means of a gradient based algorithm. Moreover, in order to avoid getting trapped in local minima, the set of data projections is randomly changed during algorithm iterations. This allows to modify the nonconvex objective and its local minima, without changing global ones, resulting in an efficient and robust algorithm.

Results obtained in the context of 3D deconvolution widefield microscopy will be presented with comparisons to other competing methods. Moreover, in order to enhance axial resolution of the deconvolved images, we employ an original strategy that consists in learning a dictionary from the highly resolved lateral sections (x,y) and apply it in both lateral and axial directions.

[1] Pedram Pad, Farnood Salehi, Elisa Celis, Patrick Thiran and Michael Unser. *Dictionary Learning Based on Sparse Distribution Tomography. *Proceedings of the 34th International Conference on Machine Learning 2017.

**Slides: PDF**