The Mirror Transform

This paper explains how to describe any finite-energy signal through a unique representation consisting of an ordered set positions and sparse signals. is obtained by designing iterative decomposition series mirror operations around those positions. The purpose find at step the location that provides for maximum decoupling between even odd components with respect it. By limiting such on three separate information bearing support, algorithm can be iterated infinity determining sequence per determines optimal energy strategy each stage providing remarkable sparsity in representation. resulting transformation leads 1-to-1 mapping. approach easily extended sequences, particular sequences finite length $N$, most notation="LaTeX">$N$ iterations are required. Thanks representation, experimental simulations demonstrate superior approximation capabilities this proposed non-linear Mirror Transform potential application many domains as coding. Its implementation has been made publicly available.