Wigner distribution associated with linear canonical transform of generalized 2-D analytic signals

Analytic complex signals find numerous applications in image and signal processing community. This article focuses on the discussion and definitions of three generalized two-dimensional (2-D) analytic signals (GASs). It begins by explaining the parametric Hilbert transform (PHT) and parametric Riesz transform (PRT), derived from analyzing the irrotational and solenoidal vector fields, respectively. Furthermore, the article explores the four-dimensional Wigner distributions associated with the linear canonical transform (WDLs) for these GASs. Finally, the advantages of these GASs are demonstrated through their application in envelope detection, and highlighting these WDLs potential for feature extraction. This article provides valuable insights into the field of 2-D analytic signals and their applications in various domains.