Projected Newton method for noise constrained ℓp regularization. (3rd December 2020)

• Record Type: Journal Article
• Authors: Cornelis, J; Vanroose, W
• Is Part Of: Inverse problems. Volume 36:Number 12(2020)
• Publication Date: 2020-12-03
• Subjects: Newton's method -- generalized Krylov subspace -- ℓp regularization -- discrepancy principle -- total variation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abb2fc
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Choosing an appropriate regularization term is necessary to obtain a meaningful solution to an ill-posed linear inverse problem contaminated with measurement errors or noise. The ℓ p norm covers a wide range of choices for the regularization term since its behavior critically depends on the choice of p and since it can easily be combined with a suitable regularization matrix. We develop an efficient algorithm that simultaneously determines the regularization parameter and corresponding ℓ p regularized solution such that the discrepancy principle is satisfied. We project the problem on a low-dimensional generalized Krylov subspace and compute the Newton direction for this much smaller problem. We illustrate some interesting properties of the algorithm and compare its performance with other state-of-the-art approaches using a number of numerical experiments, with a special focus of the sparsity inducing ℓ 1 norm and edge-preserving total variation regularization.