Multi-parameter Approaches in Image Processing

Natural images often exhibit a highly complex structure that is difficult to describe using a single regularization term. Instead, many variational models for image restoration rely on different regularization terms in order to capture the different components of the image in question. While the resulting multipenalty approaches have in principle a greater potential for accurate image reconstructions than single-penalty models, their practical performance relies heavily on a good choice of the regularization parameters. In this chapter, we provide a brief overview of existing multipenalty models for image restoration tasks. Moreover, we discuss different approaches to the problem of multiparameter selection. For the numerical examples, we will focus on the balanced discrepancy principle and the L-hypersurface method applied to PDE-based image denoising problems.