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This paper explores a Bayesian theoretic approach to constructing multiscale complex-phase-order representations. We formulate the construction of complex-phase-order representations at different structural scales based on the scale-space theory. Linear and nonlinear deterministic approaches are explored, and a Bayesian theoretic approach is introduced for constructing representations in such a way that strong structure localization and noise resilience are achieved. Experiments illustrate its potential for constructing robust multiscale complex-phase-order representations with well-localized structures across all scales under high-noise situations. Illustrative examples of applications of the proposed approach is presented in the form of multimodal image registration and feature extraction.