This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledge are available. In each case, we provide conditions (in terms of the number of measurements) for stable signal recovery from structured corruption with added unstructured noise. Our results theoretically demonstrate how to choose the regularization parameters in both partially and fully penalized recovery procedures and shed some light on the relationships among the three procedures. The key ingredient in our analysis is an extended matrix deviation inequality for isotropic sub-Gaussian matrices, which implies a tight lower bound for the restricted singular value of the extended sensing matrix. Numerical experiments are presented to verify our theoretical results.
We consider the problem of resolving r point sources from n samples at the low end of the spectrum when point spread functions (PSFs) are not known. Assuming that the spectrum samples of the PSFs lie in low dimensional subspace (let s denote the dimension), this problem can be reformulated as a matrix recovery problem. By exploiting the low rank structure of the vectorized Hankel matrix associated with the target matrix, a convex approach called Vectorized Hankel Lift is proposed in this paper. It is shown that n rs log 4 n samples are sufficient for Vectorized Hankel Lift to achieve the exact recovery. In addition, a new variant of the MUSIC method available for spectrum estimation in the multiple snapshots scenario arises naturally from the vectorized Hankel lift framework, which is of independent interest.
Abstract-This paper studies the problem of accurately recovering a structured signal from a small number of corrupted subGaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledge are available. In each case, we provide conditions for stable signal recovery from structured corruption with added unstructured noise. The key ingredient in our analysis is an extended matrix deviation inequality for isotropic sub-Gaussian matrices.
Reusing existing datasets is of considerable significance to researchers and developers. Dataset search engines help a user find relevant datasets for reuse. They can present a snippet for each retrieved dataset to explain its relevance to the user's data needs. This emerging problem of snippet generation for dataset search has not received much research attention. To provide a basis for future research, we introduce a framework for quantitatively evaluating the quality of a dataset snippet. The proposed metrics assess the extent to which a snippet matches the query intent and covers the main content of the dataset. To establish a baseline, we adapt four state-of-the-art methods from related fields to our problem, and perform an empirical evaluation based on real-world datasets and queries. We also conduct a user study to verify our findings. The results demonstrate the effectiveness of our evaluation framework, and suggest directions for future research.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.