Spatially Adaptive Filtering as Regularization in Inverse Imaging: Compressive Sensing, Super-Resolution, and Upsampling
In this chapter, the authors provide an overview of the versatile approach, with particular emphasis on three challenging and important imaging applications: inversion from sparse or limited-angle tomographic projections, image reconstruction from low-frequency or undersampled data, image and video super-resolution. They also provide formal definitions of the observation model and of the reconstruction algorithm for a rather general case. The authors discuss the application of spatially adaptive filters as regularization constraint in inverse imaging problems. The developments in image and video denoising have brought a new generation of filtering algorithms achieving unprecedented restoration quality. A priori assumptions on the image to be reconstructed are essential for any inverse imaging algorithm. In the standard variational approaches, these assumptions are usually given as penalty terms that serve as regularization in an energy criterion to be minimized. The authors demonstrate application of their approach to the inversion from sparse or limited-angle tomographic projections, image upsampling, and image/video super-resolution.