Representation of signals and images by complex coefficient weighted singularity functions

Previously proposed singularity function models are suitable only for representing real data. However, in a number of application domains such as magnetic resonance imaging, the initial raw data are complex images, which requires new image models for representing them. In this paper, a novel singularity function analysis model is proposed that represents a complex discrete signal or image as a linear complex coefficient weighted combination of singularity functions. The interest of such model is investigated in the case of high-resolution image reconstruction problems. The results show that the thus obtained reconstruction approach provides significantly better performance than existing reconstruction techniques.