This paper studies the algorithms that reconstruct a signal from its wavelet extrema representation. We show that the existing reconstruction algorithms are inadequate in assuring a consistent reconstruction. We further propose a method that can be used with a number of existing algorithms to guarantee a consistent reconstruction. The new method provides a rigorous way to prevent artifacts resulting from the spurious wavelet extrema in the reconstructed signal.
"Consistent signal reconstruction from wavelet extrema representation", Proc. SPIE 3169, Wavelet Applications in Signal and Image Processing V, (30 October 1997); doi: 10.1117/12.292795; https://doi.org/10.1117/12.292795