Complex-valued wavelet lifting transforms for signal processing
29th March 2019, 3:00 pm – 3:45 pm
Main Maths Building, SM3
Since the nineties, traditional wavelets have been successfully used for many data analysis tasks, due to their attractive compression properties as well as their flexibility. However, they are limited to situations where the data are regularly-spaced and of a certain length, and so wavelet-like lifting schemes were developed to address these drawbacks. In this talk I will discuss some recent work on complex-valued lifting transforms, which extend established wavelet lifting schemes to the complex domain, using a carefully chosen pair of data filters for analysis. The resulting transform can be applied for real-valued as well as complex-valued signal analysis, and brings benefits in a number of analysis tasks. I will highlight some of the properties of the new tools arising from these constructions, and demonstrate them on some signals drawn from different application areas.