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Restoration and separation of piecewise polynomial signals. Application to Atomic Force Microscopy

Abstract : This thesis handles several inverse problems occurring in sparse signal processing. The main contributions include the conception of algorithms dedicated to the restoration and the separation of sparse signals, and their application to force curve approximation in Atomic Force Microscopy (AFM), where the notion of sparsity is related to the number of discontinuity points in the signal (jumps, change of slope, change of curvature). In the signal processing viewpoint, we propose sub-optimal algorithms dedicated to the sparse signal approximation problem based on the ℓ0 pseudo-norm : the Single Best Replacement algorithm (SBR) is an iterative "forward-backward" algorithm inspired from existing Bernoulli-Gaussian signal restoration algorithms. The Continuation Single Best Replacement algorithm (CSBR) is an extension providing approximations at various sparsity levels. We also address the problem of sparse source separation from delayed mixtures. The proposed algorithm is based on the prior application of CSBR on every mixture followed by a matching procedure which attributes a label for each peak occurring in each mixture. Atomic Force Microscopy (AFM) is a recent technology enabling to measure interaction forces between nano-objects. The force-curve analysis relies on piecewise parametric models. We address the detection of the regions of interest (the pieces) where each model holds and the subsequent estimation of physical parameters (elasticity, adhesion forces, topography, etc.) in each region by least-squares optimization. We finally propose an alternative approach in which a force curve is modeled as a mixture of delayed sparse sources. The research of the source signals and the delays from a force-volume image is done based on a large number of mixtures since there are as many mixtures as the number of image pixels.
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Contributor : Junbo Duan <>
Submitted on : Saturday, December 4, 2010 - 9:33:50 PM
Last modification on : Friday, October 23, 2020 - 8:38:04 AM
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  • HAL Id : tel-01746376, version 2



Junbo Duan. Restoration and separation of piecewise polynomial signals. Application to Atomic Force Microscopy. Signal and Image processing. Université Henri Poincaré - Nancy 1, 2010. English. ⟨NNT : 2010NAN10082⟩. ⟨tel-01746376v2⟩



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