Wavelet methods for shape perception in electro-sensing

This paper aims at presenting a new approach to the electro-sensing problem using wavelets. It provides an efficient algorithm for recognizing the shape of a target from micro-electrical impedance measurements. Stability and resolution capabilities of the proposed algorithm are quantified in numerical simulations. Mathematics Subject Classification (MSC2000): 35R30, 35B30

[1]  I. Daubechies,et al.  A new technique to estimate the regularity of refinable functions , 1996 .

[2]  Edward H. Kingsley Bernstein polynomials for functions of two variables of class , 1951 .

[3]  David Isaacson,et al.  Electrical Impedance Tomography , 1999, SIAM Rev..

[4]  Josselin Garnier,et al.  Modeling Active Electrolocation in Weakly Electric Fish , 2012, SIAM J. Imaging Sci..

[5]  A. Quarteroni,et al.  Approximation results for orthogonal polynomials in Sobolev spaces , 1982 .

[6]  Stéphane Mallat,et al.  A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition , 2008 .

[7]  Josselin Garnier,et al.  Tracking of a Mobile Target Using Generalized Polarization Tensors , 2013, SIAM J. Imaging Sci..

[8]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[9]  A. Cohen Numerical Analysis of Wavelet Methods , 2003 .

[10]  Eung Je Woo,et al.  Mathematical framework for a new microscopic electrical impedance tomography system , 2011 .

[11]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[12]  Josselin Garnier,et al.  Generalized polarization tensors for shape description , 2014, Numerische Mathematik.

[13]  Ohin Kwon,et al.  A real time algorithm for the location search of discontinuous conductivities with one measurement , 2002 .

[14]  Josselin Garnier,et al.  Target Identification Using Dictionary Matching of Generalized Polarization Tensors , 2014, Found. Comput. Math..

[15]  H. Ammari Mathematical and Statistical Methods for Multistatic Imaging , 2013 .

[16]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[17]  Michael C. McAlpine,et al.  Electrical detection of pathogenic bacteria via immobilized antimicrobial peptides , 2010, Proceedings of the National Academy of Sciences.

[18]  Josselin Garnier,et al.  Shape recognition and classification in electro-sensing , 2014, Proceedings of the National Academy of Sciences.

[19]  Yves Capdeboscq,et al.  OPTIMAL ASYMPTOTIC ESTIMATES FOR THE VOLUME OF INTERNAL INHOMOGENEITIES IN TERMS OF MULTIPLE BOUNDARY MEASUREMENTS , 2003 .