Functional deconvolution in a periodic setting: Uniform case
By Marianna Pensky, Theofanis Sapatinas. 2007
51 citations recorded by the source corpus.
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover initial or boundary conditions on the basis of observations from a noisy solution of a partial differential equation. In the case when it is observed at a finite number of distinct points, the proposed functional deconvolution model can also be viewed as a multichannel deconvolution model. We derive minimax lower bounds for the L 2 -risk in the proposed functional deconvolution model when f(·) is assumed to belong to a Besov ball and the blurring function is assumed to possess some smoothness properties, including both regular-smooth and super-smooth convolutions. Furthermore, we propose an adaptive wavelet estimator of f(·) that is asymptotically optimal (in the minimax sense), or near-optimal within a logarithmic factor, in a wide range of Besov balls. In addition, we consider a discretization of the proposed functional deconvolution model and investigate when the availability of continuous data gives advantages over observations at the asymptotically large number of points. As an illustration, we discuss particular examples for both continuous and discrete settings.
Subfields: Computer Vision and Pattern Recognition, Mathematical Physics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/85631ecda475ecfa326bbeb9c067462f7b003e51
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In Computer Vision and Pattern Recognition
- Karim Lounici
- Richard Nickl
- Adam D. Bull
- D. Chetverikov
- Evarist Gin'e
- Kolyan Ray
- Sara A. van de Geer
In Mathematical Physics
In Numerical Analysis
- Karim Lounici
- Richard Nickl
- Evarist Gin'e
- Sara A. van de Geer
- Tengyuan Liang
- Bharath K. Sriperumbudur
Citations in the corpus
- GLOBAL UNIFORM RISK BOUNDS FOR WAVELET DECONVOLUTION ESTIMATORS (2011, methodology): “It has been extensively studied: we refer to Carroll and Hall [9], Stefanski [37], Stefanski and Carroll [38], Fan [14, 15], Diggle and Hall [12], Goldenshluger [22], Pensky and Vidakovic [36], Delaigle and Gijbels [11], Hesse and Meister [24], Johnstone et al. [25], Johnstone and Raimondo [26], Bis”