Back to Search
Start Over
Variable order smoothness priors for ill-posed inverse problems
- Source :
- Scopus-Elsevier
-
Abstract
- In this article we discuss ill-posed inverse problems, with an emphasis on hierarchical variable order regularization. Traditionally, smoothness penalties in Tikhonov regularization assume a fixed degree of regularity of the unknown over the whole domain. Using a Bayesian framework with hierarchical priors, we derive a prior model, formally represented as a convex combination of autoregressive (AR) models, in which the parameter controlling the mixture of the AR models can dynamically change over the domain of the signal. Moreover, the mixture parameter itself is an unknown and is to be estimated using the data. Also, the variance of the innovation processes in the AR model is a free parameter, which leads to conditionally Gaussian priors that have been previously shown to be much more flexible than the traditional Gaussian priors, capable, e.g., to deal with sparsity type prior information. The suggested method, the Weighted Variable Order Autoregressive model (WVO-AR) is tested with a computed example. Fil: Calvetti, Daniela. Case Western Reserve University; Estados Unidos Fil: Somersalo, Erkki. Case Western Reserve University; Estados Unidos Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentina
- Subjects :
- Well-posed problem
Inverse problems
Mathematical optimization
Algebra and Number Theory
Smoothness (probability theory)
Matemáticas
Applied Mathematics
Inverse problem
Markov autoregresive models
ill-conditioned
Matemática Pura
Computational Mathematics
Order (business)
Prior probability
Bayesian models
CIENCIAS NATURALES Y EXACTAS
Variable (mathematics)
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Scopus-Elsevier
- Accession number :
- edsair.doi.dedup.....e0301476fc9610e14b76398bd2925e1a