An optimal variable exponent model for Magnetic Resonance Images denoising

Abstract

• A novel PDE-constrained optimization problem is proposed for MRI denoising task. • The proposed optimization procedure computes the variable exponent and the clean image for MRI images. • The comparative results demonstrates the performance on two MRI datasets This paper investigates a novel PDE-constrained optimization model with discontinuous variable exponent p ( x ) identification. Since the parameter p is always related to a better approximation of the image gradient, its computation plays a critical role in preserving the image texture. Analytically, we include results on the approximation of this parameter as well as the resolution of the encountered PDE in a well posed framework. In addition, to resolve the PDE-constrained minimization problem, we proposed a modified primal-dual algorithm. Finally, numerical results are provided to compute the parameter p and also to remove high intensity of noise. The proposed algorithm simultaneously keep safe fine details and important features in medical image applications (Magnetic Resonance Images (MRI)) with numerous comparisons to show the performance of the proposed approach.