| Paper ID | D4-S4-T3.1 |
| Paper Title |
Multiple Support Recovery Using Very Few Measurements Per Sample |
| Authors |
Lekshmi Ramesh, Chandra R. Murthy, Himanshu Tyagi, Indian Institute of Science, Bangalore, India |
| Session |
D4-S4-T3: Sparse Recovery |
| Chaired Session: |
Thursday, 15 July, 23:00 - 23:20 |
| Engagement Session: |
Thursday, 15 July, 23:20 - 23:40 |
| Abstract |
In the problem of multiple support recovery, we are given access to linear measurements of multiple sparse samples in $\mathbb{R}^{d}$. These samples can be partitioned into $\ell$ groups, with samples having the same support belonging to the same group. For a given budget of $m$ measurements per sample, the goal is to recover the $\ell$ underlying supports, in the absence of the knowledge of group labels. We study this problem with a focus on the \emph{measurement-constrained} regime where $m$ is smaller than the support size $k$ of each sample. We design a two-step procedure that estimates the union of the underlying supports first, and then uses a spectral algorithm to estimate the individual supports. Our proposed estimator can recover the supports with $m
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