Variational algorithms to remove stationary noise. Application to microscopy imaging.

Jérôme Fehrenbach (1) , Pierre Weiss (1) , Corinne Lorenzo (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 ITAV - Institut des Technologies Avancées en sciences du Vivant

A framework and an algorithm are presented in order to remove stationary noise from images. This algorithm is called VSNR (Variational Stationary Noise Remover). It can be interpreted both as a restoration method in a Bayesian framework and as a cartoon+texture decomposition method. In numerous denoising applications the white noise assumption fails: structured patterns (e.g. stripes) appear in the images. The model described here addresses these cases. Applications are presented with images acquired using different modalities: scan- ning electron microscope, FIB-nanotomography, and an emerging fluorescence microscopy technique called SPIM (Selective Plane Illumination Microscope).

Mots clés: texture-geometry decom- positions; Stripe removal; non linear filtering; fast algo- rithms; total variation; Gabor filter; SPIM microscope; scanning electron microscope; nanotomography; texture-geometry decom- positions.

Domaines: Optimisation et contrôle [math.OC]; Organisation et fonctions cellulaires [q-bio.SC]; Analyse numérique [cs.NA]; Optique [physics.optics]

Jérôme Fehrenbach, Pierre Weiss, Corinne Lorenzo. Variational algorithms to remove stationary noise. Application to microscopy imaging.. IEEE Transactions on Image Processing, 2012, 21 (10), pp.4420 - 4430. ⟨10.1109/TIP.2012.2206037⟩. ⟨hal-00613097v3⟩