Statistical Multiresolution Dantzig Estimation in Imaging: Fundamental Concepts and Algorithmic Framework

Details Statistical Multiresolution Dantzig Estimation in Imaging: Fundamental Concepts and Algorithmic Framework Statistical Multiresolution Dantzig Estimation in Imaging: Fundamental Concepts and Algorithmic Framework

2011-01-23

arxiv.org/abs/1101.4373v3

Electron. J. Stat. 6 (2012) 231-268

Statistics

Applications

Scientific paper

10.1214/12-EJS671

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 supremum-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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