19 research outputs found
Exact Recovery Conditions for Sparse Representations with Partial Support Information
We address the exact recovery of a k-sparse vector in the noiseless setting
when some partial information on the support is available. This partial
information takes the form of either a subset of the true support or an
approximate subset including wrong atoms as well. We derive a new sufficient
and worst-case necessary (in some sense) condition for the success of some
procedures based on lp-relaxation, Orthogonal Matching Pursuit (OMP) and
Orthogonal Least Squares (OLS). Our result is based on the coherence "mu" of
the dictionary and relaxes the well-known condition mu<1/(2k-1) ensuring the
recovery of any k-sparse vector in the non-informed setup. It reads
mu<1/(2k-g+b-1) when the informed support is composed of g good atoms and b
wrong atoms. We emphasize that our condition is complementary to some
restricted-isometry based conditions by showing that none of them implies the
other.
Because this mutual coherence condition is common to all procedures, we carry
out a finer analysis based on the Null Space Property (NSP) and the Exact
Recovery Condition (ERC). Connections are established regarding the
characterization of lp-relaxation procedures and OMP in the informed setup.
First, we emphasize that the truncated NSP enjoys an ordering property when p
is decreased. Second, the partial ERC for OMP (ERC-OMP) implies in turn the
truncated NSP for the informed l1 problem, and the truncated NSP for p<1.Comment: arXiv admin note: substantial text overlap with arXiv:1211.728
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Automated Force Volume Image Processing for Biological Samples
Atomic force microscopy (AFM) has now become a powerful technique for investigating on a molecular level, surface forces, nanomechanical properties of deformable particles, biomolecular interactions, kinetics, and dynamic processes. This paper specifically focuses on the analysis of AFM force curves collected on biological systems, in particular, bacteria. The goal is to provide fully automated tools to achieve theoretical interpretation of force curves on the basis of adequate, available physical models. In this respect, we propose two algorithms, one for the processing of approach force curves and another for the quantitative analysis of retraction force curves. In the former, electrostatic interactions prior to contact between AFM probe and bacterium are accounted for and mechanical interactions operating after contact are described in terms of Hertz-Hooke formalism. Retraction force curves are analyzed on the basis of the Freely Jointed Chain model. For both algorithms, the quantitative reconstruction of force curves is based on the robust detection of critical points (jumps, changes of slope or changes of curvature) which mark the transitions between the various relevant interactions taking place between the AFM tip and the studied sample during approach and retraction. Once the key regions of separation distance and indentation are detected, the physical parameters describing the relevant interactions operating in these regions are extracted making use of regression procedure for fitting experiments to theory. The flexibility, accuracy and strength of the algorithms are illustrated with the processing of two force-volume images, which collect a large set of approach and retraction curves measured on a single biological surface. For each force-volume image, several maps are generated, representing the spatial distribution of the searched physical parameters as estimated for each pixel of the force-volume image
Ultrasonic non destructive testing based on sparse deconvolution
Abstract. The acoustic modality yields non destructive testing techniques of choice for indepth investigation. Given a precise model of acoustic wave propagation in materials of possibly complex structures, acoustical imaging amounts to the so-called acoustic wave inversion. A less ambitious approach consists in processing pulse-echo data (typically, A-or B-scans) to detect localised echoes with the maximum temporal (and lateral) precision. This is a resolution enhancement problem, and more precisely a sparse deconvolution problem which is naturally addressed in the inversion framework. The paper focuses on the main sparse deconvolution methods and algorithms, with a view to apply them to ultrasonic non-destructive testing