Support Driven Wavelet Frame-based Image Deblurring

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.