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Atmospheric turbulence perturbates to a great extent the optical path of incoming light from outer space thereby limiting the resolution power of capturing devices. One of the most common techniques used in astronomical imaging to compensate for this perturbation is Adaptive Optics (AO). In this paper we explore the potential of Microcanonical Multiscale Formalism (MMF) for the reconstruction of the perturbated wavefront, from the low-resolution acquisition of the turbulent phase by a Hartmann-Shack wavefront sensor used in AO. In fact, turbulent flows, although chaotic in nature, are characterised by scale hierarchy and develop cascade like structures where transfer of energy takes place from one scale to the other. We make use of MMF to infer properties along the scales of the complex signal consisting of optical phase perturbation and perform reconstruction using an appropriate wavelet decomposition associated to the cascading properties of the turbulent flow.