A nonuniform, shift-invariant, and optimal algorithm for Malvar's wavelet decomposition

In this article, we propose a new decomposition scheme for Malvar's wavelet representation. Our algorithm is nonuniform, shift-invariant and minimal for an information cost function, contrary to the shift-invariant algorithm of Cohen. We propose some restrictions to our algorithm in order to reduce the complexity and permitting us to provide some partitions of the signal in agreement with its structure. This new local trigonometric transform, more adapted than Malvar's decomposition, allows the analysis of the signal and permits one to obtain a satisfying time-frequency representation.