English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Many imaging problems require solving an inverse problem that isill-conditioned or ill-posed. Imaging methods typically address this difficultyby regularising the estimation problem to make it well-posed. This oftenrequires setting the value of the so-called regularisation parameters thatcontrol the amount of regularisation enforced. These parameters are notoriouslydifficult to set a priori, and can have a dramatic impact on the recoveredestimates. In this work, we propose a general empirical Bayesian method forsetting regularisation parameters in imaging problems that are convex w.r.t.the unknown image. Our method calibrates regularisation parameters directlyfrom the observed data by maximum marginal likelihood estimation, and cansimultaneously estimate multiple regularisation parameters. Furthermore, theproposed algorithm uses the same basic operators as proximal optimisationalgorithms, namely gradient and proximal operators, and it is thereforestraightforward to apply to problems that are currently solved by usingproximal optimisation techniques. Our methodology is demonstrated with a rangeof experiments and comparisons with alternative approaches from the literature.The considered experiments include image denoising, non-blind imagedeconvolution, and hyperspectral unmixing, using synthesis and analysis priorsinvolving the L1, total-variation, total-variation and L1, andtotal-generalised-variation pseudo-norms. A detailed theoretical analysis ofthe proposed method is presented in the companion paper arXiv:2008.05793.

Maximum likelihood estimation of regularisation parameters in  high-dimensional inverse problems: an empirical Bayesian approach. Part I:  Methodology and Experiments