BEHAVIOR OF GREEDY SPARSE REPRESENTATION ALGORITHMS ON NESTED SUPPORTS

© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This article was accepted for publication by IEEE in: Proc IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013), Vancouver, Canada, 26-31 May 2013. pp. 5710-5714

On Theorem 10 in "On Polar Polytopes and the Recovery of Sparse Representations" (vol 50, pg 2231, 2004)

(c)2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Published version: IEEE Transactions on Information Theory 59 (8): 5206-5209, Aug 2013. doi:10.1109/TIT.2013.225929

INK-SVD: LEARNING INCOHERENT DICTIONARIES FOR SPARSE REPRESENTATIONS

© 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Set up of a methodology for participatory plant breeding in bread wheat in France

In Organic Agriculture, cultivation environments and agronomic practices are very diverse. This diversity can be handled with decentralized selection based on the knowledge of farmers and scientists. A collaborative work between associations from Réseau Semences Paysannes and the DEAP team from INRA du Moulon set up an innovative breeding approach on farm based on decentralization and participation of farmers. This approach makes it possible to (i) create new population varieties of bread wheat locally adapted (genetic innovation) (ii) set up an organizational scheme based on decentralization and co construction between actors (societal innovation) and (iii) develop experimental designs, create statistical and data management tools which stimulate these genetic and societal innovations

Dictionary learning via projected maximal exploration

This work presents a geometrical analysis of the Large Step Gradient Descent (LGD) dictionary learning algorithm. LGD updates the atoms of the dictionary using a gradient step with a step size equal to twice the optimal step size. We show that the large step gradient descent can be understood as a maximal exploration step where one goes as far away as possible without increasing the the error. We also show that the LGD iteration is monotonic when the algorithm used for the sparse approximation step is close enough to orthogonal

Recovery of nested supports by greedy sparse representation algorithms over non-normalized dictionaries

We prove that if Orthogonal Matching Pursuit (OMP) recovers all s-sparse signals for a given dictionary, then it also recovers all s 0 -sparse signals on the same dictionary for any s 0 < s. We also extend Tropp’s Exact Recovery Condition (ERC) to dictionaries with non-normalized atoms. Our result does not contradict an earlier result stating that there are dictionaries and cardinalities s 0 < s such that all s-size supports satisfy Tropp’s (ERC) but not all s 0 -size supports do: that result was proved using non-normalized dictionaries and in that case Tropp’s ERC is not linked to the recovery by OMP