Solving Complex Quadratic Systems with Full-Rank Random Matrices

14 Feb 2019Shuai HuangSidharth GuptaIvan Dokmanić

We tackle the problem of recovering a complex signal $\boldsymbol x\in\mathbb{C}^n$ from quadratic measurements of the form $y_i=\boldsymbol x^*\boldsymbol A_i\boldsymbol x$, where $\{\boldsymbol A_i\}_{i=1}^m$ is a set of full-rank, complex random matrices with rotation invariant entries. This non-convex problem is related to the well understood phase retrieval problem where $\boldsymbol A_i$ is a rank-1 positive semidefinite matrix... (read more)

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