Iterative Mirror Decomposition for Signal Representation

In this paper it is shown how to describe any finite-energy continuous or discrete signal through an ordered set of positions to uniquely represent it. This is obtained by designing an iterative decomposition through a series of mirror operations around those positions. The purpose is to find at any step of the decomposition the location that provides for the maximum decoupling between the even and odd components of the signal with respect to it. The algorithm can then be iterated at infinity determining a sequence of positions. The per location information determines the optimal energy decoupling strategy at each stage providing remarkable sparsity in the representation. Thanks to the sparsity of the resulting representation, experimental simulations demonstrate superior approximation capabilities of this proposed non-linear mirror transform.