Towards hyperparameter optimization of sparse bayesian learning based on Stein’s unbiased risk estimator
Résumé
Sparse Bayesian Learning (SBL) stands as a widely
utilized compressed sensing technique wherein the sparsityinducing prior for the unknowns within the underdetermined
linear system is characterized by a Gaussian scale mixture. This
formulation results in several hyperparameters, which encompass the variance profile, noise variance, and potentially other
parameters within the variance profile priors. Traditionally, these
hyperparameters are determined via Type I or Type II Maximum
Likelihood (ML) estimation methods. In this paper, we introduce
SURE SBL, wherein the optimization of hyperparameters (as
opposed to mere estimation) relies on Stein’s Unbiased Risk
Estimator (SURE). Notably, the primary performance criterion
typically centers on the Mean Squared Error (MSE) of the
sparse parameters or the resultant signal model. We conduct
a review of the SURE approach. Subsequently, we apply the
SURE approach to assess the MSE of the sparse parameters (the
input to the linear model) and observe that it produces identical
hyperparameter optimization outcomes as those obtained via
Type II ML. Furthermore, we propose extending the SURE
approach to the output level of the linear model. Remarkably,
in the context of the large system limit, this extension yields
equivalent hyperparameter optimization outcomes concerning the
input to the linear model; however, when measurement noise is
present, the results obtained by the two kinds of SURE optimizers
diverge from those obtained through MSE optimization.
Domaines
Informatique [cs]Origine | Fichiers produits par l'(les) auteur(s) |
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