Adaptive Regularization for Image Reconstruction from Subsampled Data

Choices of regularizationRegularization parameters are central to variational methods Variational method for image restoration Image restoration . In this paper, a spatially adaptive (or distributed) regularization Regularization scheme is developed based on localized residuals, which properly balances the regularization Regularization weight between regions containing image details and homogeneous regions. Surrogate iterative methods Surrogate iterative method are employed to handle given subsampled data in transformed domains, such as Fourier or wavelet data. In this respect, this work extends the spatially variant regularization Regularization technique previously established in Dong et al. (J Math Imaging Vis 40:82–104, 2011), which depends on the fact that the given data are degraded images only. Numerical experiments for the reconstruction from partial Fourier data Partial Fourier data and for wavelet inpainting Wavelet inpainting prove the efficiency of the newly proposed approach.