Section: New Results

Exact continuous penalties for ${\ell }_2$-${\ell }_0$ minimization: Application to Photo Activated Localization Microscopy (PALM)

Participants : Simon Gazagnes, Emmanuel Soubies, Laure Blanc-Féraud.

In conventional microscopy techniques, the spatial resolution of an image is limited by the diffraction phenomena. Recent methods like photo-activated localization microscopy (PALM) allow high-precision molecule localization by sequentially activating and imaging a small random set of fluorescent molecules in the sample. However, the quality of this super-resolved image is related to the density of emitters activated at each acquisition and the numerical method used to locate molecules.

Applications for these microscopy techniques are then mainly restricted by the number of acquisitions required to obtain the superresolved image. One way to overcome this limitation is to increase the density of emitters activated at each acquisition. Nevertheless, it will cause overlapping for a certain number of spots on the acquired image which makes the localization of the underlying molecules a harder task. Considering such a high density setting, we have proposed to perform the molecules localization by solving a ${\ell }_0$-penalized least squares criteria through the minimization of the Continuous Exact ${\ell }_0$ (CEL0) relaxation that we have previously proposed. The method has provided interesting results, competing with state of the art methods, as shown on Figure 2. This work has been submitted for the conference ISBI 2017.

Figure 2. From left to right: Conventional Wide Field image, PALM with DAOSTORM (state of the art algorithm) reconstruction, PALM with the proposed reconstruction.