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