62
Views
0
CrossRef citations to date
0
Altmetric
Articles

Adaptive discretization for signal detection in statistical inverse problems

Pages 494-505 | Received 16 Dec 2013, Accepted 28 Feb 2014, Published online: 03 Apr 2014
 

Abstract

We discuss statistical tests in inverse problems when the original equation is replaced by a discretized one, i.e. a linear system of equations. Previous studies revealed that using the discretization level as regularizing procedure is possible, but its application is limited unless discretization is restricted to the singular value decomposition, see C. Marteau and P. Mathé, General regularization schemes for signal detection in inverse problems, 2013. General linear regularization may circumvent this, and we propose a regularization of the discretized equations. The discretization level may be chosen adaptively, which may save computational budget. This results in tests which are known to yield the optimal separation rate up to some constant in many cases.

AMS Subject Classifications:

Notes

Dedicated to Bernd Hofmann on the occasion of his 60th birthday.

1 The paradigm here is that ‘Absence of evidence is not evidence of absence’, and we refer to [Citation4].

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.