“sample complexity”

Abstract: We investigate the problem of recovering jointly \(r\)-rank and \(s\)-bisparse matrices from as few linear measurements as possible, considering arbitrary measurements as well as rank-one measurements. In both cases, we show that \(m \asymp r s \ln(en/s)\) measurements make the recovery possible in theory, meaning via a nonpractical algorithm.

Abstract: The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not require any training, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue.