Invited Session Tue.1.H 1012

Tuesday, 10:30 - 12:00 h, Room: H 1012

Cluster 17: Nonsmooth optimization [...]

Nonsmooth optimization in imaging sciences II


Chair: Dirk Lorenz



Tuesday, 10:30 - 10:55 h, Room: H 1012, Talk 1

michael goldman
Continuous primal-dual methods for image processing


In image processing, variational models are widespread. Tackling numerically these models is still a challenging
problem. Among the existing methods, the primal-dual methods are some of the most efficient. They
are however still not well understood. The aim of this work is to study the continuous primal-dual method
proposed by Appleton and Talbot. This study gives a new insight on this approach and yields original a
posteriori estimates.



Tuesday, 11:00 - 11:25 h, Room: H 1012, Talk 2

Elias Salomão Helou
Incremental subgradients for constrained convex optimization: A unified framework and new methods

Coauthor: Álvaro R. De Pierro


We will present a unifying framework for nonsmooth convex minimization bringing together ε-subgradient algorithms and methods for the convex feasibility problem. This development is a natural step for ε-subgradient methods in the direction of constrained optimization since the Euclidean projection frequently required in such methods is replaced by an approximate projection, which is often easier to compute. The developments are applied to incremental subgradient methods, resulting in new algorithms suitable to large-scale optimization problems, such as those arising in tomographic imaging.
The flexibility of the framework will be demonstrated by the presentation of several operators, both for the optimality step and for the feasibility step of the prototypical algorithm.



Tuesday, 11:30 - 11:55 h, Room: H 1012, Talk 3

Jerome Fehrenbach
Stripes removal in images, applications in microscopy

Coauthors: Corinne Lorenzo, Pierre Weiss


In a number of imaging modalities, images are degraded by a noise composed of stripes. This is the case, e.g., in Atomic Force Microscopy, in nanotomography or in Selective Plane Illumination Microscope (which is an emerging imaging modality). This work aims at proposing an efficient method to restore these images. A model of stationary noise is presented, where the noise is defined as the convolution of a given pattern with a white noise. The denoising problem is then formulated using a Bayesian approach. It leads to a non-smooth convex optimization problem. The minimization is performed using a preconditionned primal-dual algorithm proposed by Chambolle and Pock in 2011. Our framework allows to take into account several components of noise, and the proposed algorithm can simultaneously remove stripes and Gaussian white noise. Results on images obtained using different modalities are presented, using a Total Variation prior on the space of images. A plugin for the open source FIJI software is available.


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