Invariant multiresolution analysis: theory and applications
Chi‐Wah Kok, Y. Hui, Truong Q. Nguyen · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1997
The characterization and construction of translation invariant multiresolution system is discussed. Multiresolution basis that provides optimal performance in approximating functions with different translation is considered. Translation variance is defined to be the variance of the energy when projecting input signal under different translation to the vector space constructed by multiresolution basis. It is proved that the translation variant property of all the multiresolution basis onto themselves is a complete representation of the translation variant property of the multiresolution system. By considering scale limited signal expansion in multiresolution analysis, optimal signal adapted multiresolution basis function is defined. The results are used to design optimal signal adapted translation invariant multiresolution basis. Simulation results on the signal adapted translation invariant multiresolution basis in detection problems are presented. The constructed system outperforms tradition multiresolution system that uses translation variant basis.