Stein COnsistent Risk Estimator (SCORE) for hard thresholding

Charles-Alban Deledalle (1) , Gabriel Peyré (2) , Jalal M. Fadili (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Equipe Image - Laboratoire GREYC - UMR6072

In this work, we construct a risk estimator for hard thresholding which can be used as a basis to solve the difficult task of automatically selecting the threshold. As hard thresholding is not even continuous, Stein's lemma cannot be used to get an unbiased estimator of degrees of freedom, hence of the risk. We prove that under a mild condition, our estimator of the degrees of freedom, although biased, is consistent. Numerical evidence shows that our estimator outperforms another biased risk estimator.

Mots clés: hard thresholding; sparsity; risk estimation; threshold selection

Domaines: Traitement des images [eess.IV]; Applications [stat.AP]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Statistiques [math.ST]; Théorie [stat.TH]

Charles-Alban Deledalle, Gabriel Peyré, Jalal M. Fadili. Stein COnsistent Risk Estimator (SCORE) for hard thresholding. Signal Processing with Adaptive Sparse Structured Representations., Jul 2013, Lausanne, Switzerland. ⟨hal-00776303v2⟩