Best progressive tiling of the time-frequency plane based on fast time splitting and wavelet transform

In this paper we present a fast splitting algorithm (FSA) for a signal that when combined with the wavelet transform for each interval and an optimality criterion, leads to the best progressive tiling of the time-frequency plane. Given a set of basic regions and a cost function defined over this set, we find the minimum cost cover of the signal and establish the conditions for progressive analysis. We show how when progressive conditions are verified this method can be modelled with simple structures such as trellis diagrams or ordinary Petri nets. The FSA includes the splitting induced by the double tree algorithm (DTA) [8], and allows better signal analysis and coding efficiency. We also present two heuristic approaches (basis regions with bounded maximum length, and best past splitting) that can reduce properly the complexity of the FSA maintaining the improvements of the method