Journal of Multivariate Analysis
Optimal spherical deconvolution
Journal of Multivariate Analysis
Atomic Decomposition by Basis Pursuit
SIAM Review
Sharp minimaxity and spherical deconvolution for super-smooth error distributions
Journal of Multivariate Analysis
On Model Selection Consistency of Lasso
The Journal of Machine Learning Research
Sparse density estimation with l1 penalties
COLT'07 Proceedings of the 20th annual conference on Learning theory
Aggregation and sparsity via ℓ1 penalized least squares
COLT'06 Proceedings of the 19th annual conference on Learning Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
| Hi-index | 0.00 |
We consider the problem of estimating a density of probability from indirect data in the spherical convolution model. We aim at building an estimate of the unknown density as a linear combination of functions of an overcomplete dictionary. The procedure is devised through a well-calibrated @?"1-penalized criterion. The spherical deconvolution setting has been barely studied so far, and the two main approaches to this problem, namely the SVD and the hard thresholding ones considered only one basis at a time. The dictionary approach allows to combine various bases and thus enhances estimates sparsity. We provide an oracle inequality under global coherence assumptions. Moreover, the calibrated procedure that we put forward gives quite satisfying results in the numerical study when compared with other procedures.