2011/02/06 by Kazufumi Ito, Bangti Jin, Ito, Kazufumi +3
Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Statistical and numerical algorithms #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1102.1173
openalex publication_date 2011/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vector-valued) regularization parameter, and some theoretical results are presented. In particular, the consistency of the discrepancy principle as well as convergence rate are established, and an a posteriori error estimate for the balancing principle is established. Also two fixed point algorithms are proposed for computing the regularization parameter by the latter rule. Numerical results for several nonsmooth multi-parameter models are presented, which show clearly their superior performance over their single-parameter counterparts.