Multiple-constraint variational framework and image restoration problems

In this study, an advanced variational model is presented for problem modelling in computer vision and image processing. The proposed model allows for the definition of multiple constraints in data fidelity, which has not been considered in previous state-of-the-art methods. With this definition, the model is more robust and flexible with regard to problem modelling. Two algorithms are introduced to solve the optimisation problems: one for the vector domain and the other for the frequency domain. The issue of multiple L¹-norms in the data fidelity term is resolved with these algorithms; this remained unsolved in previous research because of the difficulty with optimisation. The proposed model is demonstrated through two problems in image processing: image denoising and image deblurring. The results indicate that, compared to previous methods, images of high visual quality were both produced and recovered when using the proposed model. In addition, good and stable results in real-world images were yielded by the proposed model, which indicates vast potential for practical uses.