Diffusion tensor imaging with deterministic error bounds
arXiv:1509.02223 · doi:10.1007/s10851-016-0639-7
Abstract
Errors in the data and the forward operator of an inverse problem can be handily modelled using partial order in Banach lattices. We present some existing results of the theory of regularisation in this novel framework, where errors are represented as bounds by means of the appropriate partial order. We apply the theory to Diffusion Tensor Imaging, where correct noise modelling is challenging: it involves the Rician distribution and the nonlinear Stejskal-Tanner equation. Linearisation of the latter in the statistical framework would complicate the noise model even further. We avoid this using the error bounds approach, which preserves simple error structure under monotone transformations.
References in corpus (7)
- A primal-dual hybrid gradient method for non-linear operators with applications to MRI
- A Second Order Non-Smooth Variational Model for Restoring Manifold-Valued Images
- Bilevel parameter learning for higher-order total variation regularisation models
- Maximum-A-Posteriori Estimates in Linear Inverse Problems with Log-concave Priors are Proper Bayes Estimators
- The Residual Method for Regularizing Ill-Posed Problems
- Discretization-invariant Bayesian inversion and Besov space priors
- A Generalization of the Chambolle-Pock Algorithm to Banach Spaces with Applications to Inverse Problems