Adaptive Inpainting Algorithm Based on DCT Induced Wavelet Regularization

In this paper, we propose an image inpainting optimization model whose objective function is a smoothed $\ell^{1}$ norm of the weighted nondecimated 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 nondifferentiable term, we present a basic algorithm inspired by Beck and Teboulle's recent work on the model. Based on this basic algorithm, we propose an automatic way to determine the weights involved in the model and update them in each iteration. The DCT as an orthogonal transform is used in various applications. We view the rows of a DCT matrix as the filters associated with a multiresolution analysis. Nondecimated wavelet transforms with these filters are explored in order to analyze the images to be inpainted. Our numerical experiments verify that under the proposed framework, the filters from a DCT matrix demonstrate promise for the task of image inpainting.