We introduce a new approach to wavefront phase reconstruction in Adaptive Optics using a non-linear approach derived from the Microcanonical Multiscale Formalism (MMF). MMF comes from established concepts in statistical physics, well-suited for the multiscale analysis of complex signals through the precise numerical estimate of geometrically localized singularity exponents. These exponents quantify the degree of predictability at each point of the signal domain, and provide information on the dynamics of the associated system. We show that multiresolution analysis on the singularity exponents of a high-resolution turbulent phase allows propagation along the scales of the phase gradients in low-resolution, to a higher resolution and offers an innovative approach to wavefront phase reconstruction in Adaptive Optics.