en:recherche [Guillaume ROND]

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====== Publications ======

Available also on the page [[https://www.i2m.univ-amu.fr/spip.php?page=publications&aigle_annee=&aigle_auteur=54&id_theme=&details=0&typedoc=&aigle_frame=0&module=1&aigle_item_by_page=7&offset=0|I2M]]


===== Wavelets on graphs =====
  * L. Avena, F. Castell, A. Gaudilliere, C. Melot. "Intertwining wavelets or Multiresolution analysis on graphs through random forests", Applied and Comp. Harmonic Analysis, 2018, in press.[[https://hal.archives-ouvertes.fr/hal-01877023v1|HAL]]

  * Package Python [[https://pypi.org/project/IntertwiningWavelet/|IntertwiningWavelet]] (D. Benielli, Labex Archimède)

  * L. Avena, F. Castell, A. Gaudilliere, C. Melot. "Random Forests and Networks Analysis", Journal of Statistical Physics, 2018, 173, pp. 985–1027 [[https://hal.archives-ouvertes.fr/hal-01877018|HAL]]
  * L. Avena, F. Castell, A. Gaudilliere, C. Melot. "Approximate and exact solutions of intertwining equations through random spanning forests", preprint [[https://hal.archives-ouvertes.fr/hal-01470573v1|HAL]]

===== Multifractal analysis =====
==== Pointwise exponents ====
  * P. Abry, S. Jaffard, R. Leonarduzzi, C. Melot, H. Wendt. "New exponents for pointwise singularity classification", in Proc. Fractals and Related Fields III, 19-26 September 2015, Porquerolles, France, S. Seuret and J. Barral, Eds., 2017. 
  * M. Ben Slimane, C. Melot. "Analysis of a fractal boundary: the graph of the Knopp function", Abstract and Applied Analysis, [[https://hal.archives-ouvertes.fr/hal-01037859v1|HAL]]
  * S. Jaffard, C. Melot. "Wavelet Analysis of Fractal Boundaries. Part 2: Multifractal Analysis", Communications in Mathematical Physics, Springer Verlag, 2005, 258, pp.541-565. [[https://hal.archives-ouvertes.fr/hal-01071366v1|HAL]]
  * S. Jaffard, C. Melot. "Wavelet analysis of fractal Boundaries, Part 1: Local regularity", Communications in Mathematical Physics, Springer Verlag, 2005, 258, pp.513-539. [[https://hal.archives-ouvertes.fr/hal-01071365v1|HAL]]

==== Analysis of multifractal functions ====
  * S. Jaffard, P. Abry, C. Melot, R. Leonarduzzi, H. Wendt. "Multifractal analysis based on p-exponents and lacunarity exponents", in Fractal Geometry and Stochastics V, C. Bandt et al., Eds., pp. 279-313, Series Progress in Probability, Vol. 70, Birkhäuser, 2015. [[https://hal.archives-ouvertes.fr/hal-01170037v1|HAL]]
  * C. Coiffard Marre, C. Melot, T. Willer. "A family of functions with two different spectra of singularities", in Journal of Fourier Analysis and Applications, Springer Verlag, 2014, 20 (5), pp.961-984. [[https://hal.archives-ouvertes.fr/hal-00831404v5|HAL]]
  * C. Melot "Oscillating singularities in Besov spaces", Journal de Mathématiques Pures et Appliquées, Elsevier, 2004, 83 (3), pp.367-416.[[https://hal.archives-ouvertes.fr/hal-01071363v1|HAL]]

==== Applications ====
  * R. Leonarduzzi, H. Wendt, P. Abry, S. Jaffard, C. Melot, "Finite resolution effects in p-leader multifractal analysis," IEEE T. Signal Proces., vol. 65, no. 13, pp. 3359-3368, 2017. [[https://hal.archives-ouvertes.fr/hal-01479891|HAL]]
  * S. Jaffard, C. Melot, R. Leonarduzzi, H. Wendt, P. Abry, S. G. Roux, M. E. Torres, "p-exponent and p-leaders, Part I: Negative pointwise regularity," Physica A, vol. 448, pp. 300-318, 2016. [[https://hal.archives-ouvertes.fr/hal-01180560v1|HAL]]
  * R. Leonarduzzi, H. Wendt, P. Abry, S. Jaffard, C. Melot, S. G. Roux, M. E. Torres, "p-exponent and p-leaders, Part II: Multifractal Analysis, Relations to Detrended Fluctuation Analysis", Physica A, vol. 448, pp. 319-339, 2016.[[https://hal.archives-ouvertes.fr/hal-01291278v1|HAL]]


===== Inverse problems in image processing=====
  *  C. Melot, Y. Boursier, J.F Aujol, S. Anthoine "Some proximal methods for Poisson intensity CBCT and PET", Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2012, 6 (4), p. 565-598.[[https://hal.archives-ouvertes.fr/hal-00640215v1|HAL]]
  * S. Anthoine, J. F Aujol, Y. Boursier, C. Melot. "On the efficiency of proximal methods for CBCT and PET", ICIP 2011 : 2011 IEEE International Conference on Image Processing, Sep 2011, Bruxelles, Belgium. pp.1365 - 1368, [[https://hal.archives-ouvertes.fr/in2p3-00869439v1|HAL]]
  * Y. Boursier, M. Dupont, S. Anthoine, J.F. Aujol, C. Melot. "Proximal Algorithms and CT: New Results on 3D Real Datas and Color CT", 2012 SIAM Conference on Imaging Science, Apr 2012, Philadelphie, United States [[https://hal.archives-ouvertes.fr/in2p3-00720055v1|HAL]]


===== Probability theory=====
  * F. Castell, C. Laurent, C. Melot. "Exponential moments of self-intersection local times of stable random walks in subcritical dimensions", Journal of the London Mathematical Society (2), 2014, 89 (2), pp.876-902. [[https://hal.archives-ouvertes.fr/hal-00849628v1|HAL]]