3 accepted papers
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including phase retrieval, quantum state tomography, and learning shallow neural networks with quadratic activations, among others. Our approach is to directly estimate the lo…
In many signal processing tasks, one seeks to recover an rcolumn matrix object X ϵ ℂ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n×r</sup> from a set of nonnegative quadratic measurements up to orthonormal transforms. Example applications include co…
We address the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of magnitude measurements that are quadratic in the sensing vectors in the presence of arbitrary outliers. We propose a parameter-free algorithm that seeks the PSD matrix that minimizes the ℓ1-norm of the m…