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Generalized cross validation for ℓp-ℓq minimization
- Source :
- Numerical Algorithms. 88:1595-1616
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Discrete ill-posed inverse problems arise in various areas of science and engineering. The presence of noise in the data often makes it difficult to compute an accurate approximate solution. To reduce the sensitivity of the computed solution to the noise, one replaces the original problem by a nearby well-posed minimization problem, whose solution is less sensitive to the noise in the data than the solution of the original problem. This replacement is known as regularization. We consider the situation when the minimization problem consists of a fidelity term, that is defined in terms of ap-norm, and a regularization term, that is defined in terms of aq-norm. We allow 0 <p,q≤ 2. The relative importance of the fidelity and regularization terms is determined by a regularization parameter. This paper develops an automatic strategy for determining the regularization parameter for these minimization problems. The proposed approach is based on a new application of generalized cross validation. Computed examples illustrate the performance of the method proposed.
- Subjects :
- Applied Mathematics
010103 numerical & computational mathematics
Inverse problem
01 natural sciences
Regularization (mathematics)
Cross-validation
Term (time)
010101 applied mathematics
Noise
Theory of computation
Applied mathematics
Minification
Sensitivity (control systems)
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 88
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi...........0a2bbb599fdd4fe47c968aec5ca59444