Blockwise SVD with error in the operator and application to blind deconvolution
Vareschi, Thomas; Picard, Dominique; Hoffmann, Marc; Delattre, Sylvain (2012), Blockwise SVD with error in the operator and application to blind deconvolution, Electronic Journal of Statistics, 6, p. 2274-2308. http://dx.doi.org/10.1214/12-EJS745
TypeArticle accepté pour publication ou publié
Journal nameElectronic Journal of Statistics
MetadataShow full item record
Abstract (EN)We consider linear inverse problems in a nonparametric statistical framework. Both the signal and the operator are unknown and subject to error measurements. We establish minimax rates of convergence under squared error loss when the operator admits a blockwise singular value decomposition (blockwise SVD) and the smoothness of the signal is measured in a Sobolev sense. We construct a nonlinear procedure adapting simultaneously to the unknown smoothness of both the signal and the operator and achieving the optimal rate of convergence to within logarithmic terms. When the noise level in the operator is dominant, by taking full advantage of the blockwise SVD property, we demonstrate that the block SVD procedure outperforms classical methods based on Galerkin projection or nonlinear wavelet thresholding. We subsequently apply our abstract framework to the specific case of blind deconvolution on the torus and on the sphere.
Subjects / Keywordserror in the operator; linear in- verse problems; nonparametric adaptive estimation; circular and spherical deconvolution; blockwise SVD; Blind deconvolution
Showing items related by title and author.
Muzy, Jean-François; Delattre, Sylvain; Hoffmann, Marc; Bacry, Emmanuel (2013) Article accepté pour publication ou publié
Design and rationale of the non-interventional, edoxaban treatment in routiNe clinical prActice in patients with venous ThromboEmbolism in Europe (ETNA-VTE-Europe) study Cohen, Alexander T.; Ay, Cihan; Hainaut, Philippe; Décousus, Hervé; Hoffmann, Ulrich; Gaine, Sean; Coppens, Michiel; da Silva, Pedro Marques; Jiménez, David; Amann-Vesti, Beatrice; Brüggenjürgen, Bernd; Lévy, Pierre; Bastida, Julio Lopez; Vicaut, Eric; Laeis, Petra; Fronk, Eva-Maria; Zierhut, Wolfgang; Malzer, Thomas; Bramlage, Peter; Agnelli, Giancarlo (2018) Article accepté pour publication ou publié
Derivative-Free Estimation of the Score Vector and Observed Information Matrix with Application to State-Space Models Rubenthaler, Sylvain; Jacob, Pierre E.; Doucet, Arnaud (2013) Document de travail / Working paper