  The wavelet frame systems have been playing an active role in image
restoration and many other image processing fields over the past decades, owing
to the good capability of sparsely approximating piece-wise smooth functions
such as images. In this paper, we propose a novel wavelet frame based sparse
recovery model called \textit{Support Driven Sparse Regularization} (SDSR) for
image deblurring, where the partial support information of frame coefficients
is attained via a self-learning strategy and exploited via the proposed
truncated $\ell_0$ regularization. Moreover, the state-of-the-art image
restoration methods can be naturally incorporated into our proposed wavelet
frame based sparse recovery framework. In particular, in order to achieve
reliable support estimation of the frame coefficients, we make use of the
state-of-the-art image restoration result such as that from the IDD-BM3D method
as the initial reference image for support estimation. Our extensive
experimental results have shown convincing improvements over existing
state-of-the-art deblurring methods.
