Of all the two-beam interference patterns, the ones obtained in speckle interferometry (SI) are the most difficult to be phase-demodulated. Many solutions exist in classical smooth-wave interferometry and alike techniques, both in static and dynamic regimes. In SI, the three constituents of the signals - the background, the modulation and the phase - are all basically random variables. There is no way to make a prediction of the evolution of these variables outside the small size of the correlation volumes - the volumes defined by the average speckle grain. To some extent, the classical methods can be adapted to SI. Here, we prefer to develop a series of new processing tools tailored to the specificities of the dynamic SI signals: the cooperative use of the empirical mode decomposition (EMD), the Hilbert transform (HT), and the three dimensional piecewise processing (3DPP) for recovering efficiently the phase of these signals.