This talk is about the wavelet frame-based image and video restorations. Main ideas of wavelet frame based models and algorithms for image restorations will be reviewed. Some of applications of wavelet frame based models image analysis and restorations will be shown. Examples of such applications include image and video inpainting, denoising, decomposition, image deblurring and blind debarring, image isegmentation, CT image reconstruction and etc. It is noted that, in all of these applications, spline wavelet frames derived from the unitary extension principle are used. The applying of spline wavelet tight frame approaches leads us to establishing a connection between wavelet frame base method and the total variation based method. In fact, we will show that when spline wavelet frames are used, a special case of a wavelet frame based model can be viewed as a discrete approximation at a given resolution to the total variation based method. A convergence analysis in terms of objective functionals and their approximate minimizers as image resolution increases will be discussed.
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