Clifford-Valued Ridgelet Transform: Localization Operators and Uncertainty Principles

The Clifford algebra serves as a potent generalization of both Grassmann's exterior algebra and Hamilton's quaternion algebra in the sense that they incorporate both the geometrical and algebraic features of Euclidean space into a single structure. The goal of this article is to introduce the concept of the Clifford-valued ridgelet transform in order to utilize the benefits of ridgelet transforms for an efficient representation of the Clifford-valued signals. The fundamental properties of the proposed transform are examined via the machinery of operator theory and Clifford-valued Fourier transforms. To extend the scope of the study, the boundedness of the localization operators and the uncertainty inequalities associated with the Clifford-valued ridgelet transform is also investigated in detail.