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2012 Statistical multiresolution Dantzig estimation in imaging: Fundamental concepts and algorithmic framework
Klaus Frick, Philipp Marnitz, Axel Munk
Electron. J. Statist. 6: 231-268 (2012). DOI: 10.1214/12-EJS671

Abstract

In this paper we are concerned with fully automatic and locally adaptive estimation of functions in a “signal + noise”-model where the regression function may additionally be blurred by a linear operator, e.g. by a convolution. To this end, we introduce a general class of statistical multiresolution estimators and develop an algorithmic framework for computing those. By this we mean estimators that are defined as solutions of convex optimization problems with -type constraints. We employ a combination of the alternating direction method of multipliers with Dykstra’s algorithm for computing orthogonal projections onto intersections of convex sets and prove numerical convergence. The capability of the proposed method is illustrated by various examples from imaging and signal detection.

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Klaus Frick. Philipp Marnitz. Axel Munk. "Statistical multiresolution Dantzig estimation in imaging: Fundamental concepts and algorithmic framework." Electron. J. Statist. 6 231 - 268, 2012. https://doi.org/10.1214/12-EJS671

Information

Published: 2012
First available in Project Euclid: 29 February 2012

zbMATH: 1314.62094
MathSciNet: MR2988407
Digital Object Identifier: 10.1214/12-EJS671

Subjects:
Primary: 62G05 , 90C06
Secondary: 68U10

Keywords: alternating direction method of multipliers (ADMM) , biophotonics , Dantzig selector , Dykstra’s projection algorithm , local adaption , signal detection , statistical imaging , statistical multiscale analysis , statistical regularization

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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