Bandlet Image Estimation with Model Selection

TL;DR

This paper introduces a model selection based bandlet estimator for geometrically regular images in white noise, achieving near asymptotic minimaxity and combining basis selection with bandlet approximation.

Contribution

It presents a novel bandlet estimator that integrates model selection with orthogonal basis dictionaries, providing theoretical guarantees for geometrically regular images.

Findings

Achieves near asymptotic minimaxity for regular images

Combines basis selection with bandlet approximation effectively

Provides a self-contained tutorial on model selection with orthogonal bases

Abstract

To estimate geometrically regular images in the white noise model and obtain an adaptive near asymptotic minimaxity result, we consider a model selection based bandlet estimator. This bandlet estimator combines the best basis selection behaviour of the model selection and the approximation properties of the bandlet dictionary. We derive its near asymptotic minimaxity for geometrically regular images as an example of model selection with general dictionary of orthogonal bases. This paper is thus also a self contained tutorial on model selection with orthogonal bases dictionary.