Image representation based on cosine crossings of wavelet decompositions
Prasanjit Panda, Michael L. Hilton, Bjorn D. Jawerth, Wim Sweldens · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
The sampling theorem of Bar-David provides an implicit representation of bandlimited signals using their crossings with a cosine function. This cosine function is chosen in a way that guarantees a unique representation of the signal. Previously, we extended Bar-David's theorem to periodic functions on an interval, leading to a multiplicative representation involving a Riesz product whose roots form a unique and stable representation of the signal. We also presented numerical algorithms for the analysis and synthesis of 1D signals. In this paper, we extend our previous results by developing algorithms for 2D signals and incorporating the wavelet transform into the cosine crossing representation.