An Adaptive Inpainting Algorithm Based on Dct Induced Wavelet Regularization

In this work, we propose an image inpainting optimization model whose objective functional is a smoothed l norm of the weighted non-decimated discrete cosine transform (DCT) coefficients of the underlying image. By identifying the objective function of the proposed model as a sum of a differentiable term and a non-differentiable term, we give a basic algorithm inspired by Beck and Teboulle’s recent work [1] for the proposed model. Based on this basic algorithm, we propose an automatic way to determine the weights involved in the model and update them at each iteration. The discrete cosine transform as an orthogonal transform is used in various applications. We view the rows of a discrete cosine transform matrix as the filters associated with a multiresolution analysis. Non-decimated wavelet transforms with these filters are explored to analyze images to be inpainted. Our numerical experiments verify that under the proposed framework, the filters from a discrete cosine transform matrix demonstrate promise for the task of image inpainting.