Uniform Multipenalty Regularization for Linear Ill-Posed Inverse Problems

This study examines, in the framework of variational regularization methods, a multi-penalty regularization approach which builds upon the uniform penalty (UPEN) method, previously proposed by the authors for nuclear magnetic resonance data processing. The paper introduces two iterative methods, UpenMM and GUpenMM, formulated within the majorization-minimization framework. These methods are designed to identify appropriate regularization parameters and solutions for linear inverse problems utilizing multipenalty regularization. The paper demonstrates the convergence of these methods and illustrates their potential through numerical examples, showing the practical utility of pointwise regularization terms in solving various inverse problems.