This paper considers the problem of estimating an unknown high dimensional signal from (typically low-dimensional) noisy linear measurements, where the desired unknown signal is assumed to possess a group-sparse structure, i.e. given a (pre-defined) partition of its entries into groups, only a small number of such groups are non-zero. Assuming the unknown group-sparse signal is generated according to a certain statistical model, we provide guarantees under which it can be efficiently estimated via solving the well-known group Lasso problem. In particular, we demonstrate that the set of indices for non-zero groups of the signal (called the group-level support of the signal) can be exactly recovered by solving the proposed group Lasso problem provided that its constituent non-zero groups are small in number and possess enough energy. Our guarantees rely on the well-conditioning of measurement matrix, which is expressed in terms of the block coherence parameter and can be efficiently computed. Our results are non-asymptotic in nature and therefore applicable to practical scenarios.
|Original language||English (US)|
|Title of host publication||2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||5|
|State||Published - Jun 16 2017|
|Event||2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States|
Duration: Mar 5 2017 → Mar 9 2017
|Name||ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings|
|Other||2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017|
|Period||3/5/17 → 3/9/17|
Bibliographical noteFunding Information:
This work was supported by the DTI grant, NSF Award CCF-1217751, and the DARPA Young Faculty Award N66001-14-1-4047.
© 2017 IEEE.
- Group sparsity
- group Lasso
- primal-dual witness
- structured support recovery