Abstract
The problem of sparse signal recovery from quadratic cross-correlation measurements is considered. Compared to the signal recovery problem that uses linear data, the unknown here is a matrix, X=h̊o o̊^, formed by the cross correlations of r,̊ a K-dimensional vector that is the unknown of the linear problem. Solving for X creates a bottleneck as the number of unknowns grows now quadratically in K. To solve this problem efficiently a dimension reduction approach is proposed in which the contribution of the off-diagonal terms rh̊i ρj̊^ for 퐢 neq 퐣 to the data is treated as noise and is absorbed using the Noise Collector [1]. With this approach, we recover the unknown X by solving a convex linear problem whose cost is similar to the one that uses linear measurements. © 2021 IEEE.
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