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Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix hasbecome an emerging alternative to the traditional sparse regularization, due toits ability to alleviate the basis mismatch between the true support in thecontinuous domain and the discrete grid. In this paper, we introduce a novelstructured low rank matrix framework to restore piecewise smooth functions.Inspired by the total generalized variation to use sparse higher orderderivatives, we derive that the Fourier samples of higher order derivativessatisfy an annihilation relation, resulting in a low rank multi-fold Hankelmatrix. We further observe that the SVD of a low rank Hankel matrix correspondsto a tight wavelet frame system which can represent the image with sparsecoefficients. Based on this observation, we also propose a wavelet frameanalysis approach based continuous domain regularization model for thepiecewise smooth image restoration. Finally, numerical results on imagerestoration tasks are presented as a proof-of-concept study to demonstrate thatthe proposed approach is compared favorably against several popular discreteregularization approaches and structured low rank matrix approaches.

Image Restoration: Structured Low Rank Matrix Framework for Piecewise Smooth Functions and Beyond