Higher Order Data Fidelity Norm for Enhanced Visual Quality of Restored Images

This paper proposes using higher order norms as the measure for data fidelity to improve perceived visual quality of restored images. It constructs a generic data fidelity norm that can accommodate a variety of possible norms and then casts the corresponding regularized image restoration as the minimization of an energy functional, whose minimization through steepest decent leads to the restoration PDE. Numerical simulation indicates that L¹ norm delivers the worst visual quality and PSNR. While L² norm produces the best PSNR, L³ and L⁴ norms provide better visual quality in terms of sharper edges and smoother smooth areas. It seems that visual quality improves as the order of data fidelity norm increases.