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.HAL
L. Avena, F. Castell, A. Gaudilliere, C. Melot. “Random Forests and Networks Analysis”, Journal of Statistical Physics, 2018, 173, pp. 985–1027 HAL
L. Avena, F. Castell, A. Gaudilliere, C. Melot. “Approximate and exact solutions of intertwining equations through random spanning forests”, preprint 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, 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. 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. 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. 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. HAL
C. Melot “Oscillating singularities in Besov spaces”, Journal de Mathématiques Pures et Appliquées, Elsevier, 2004, 83 (3), pp.367-416.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. 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. 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.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.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, 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 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. HAL