Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priors
Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priors
The problem of recovering a signal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x \in \mathbb{R}^{n}$</tex-math></inline-formula> from a quadratic system <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\{y_{i}=x^{⊤}\,A_{i}x,\,i=1,\dots,m\}$</tex-math></inline-formula> with full-rank matrices <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A_{i}$</tex-math></inline-formula> frequently arises in applications such as unassigned distance geometry and sub-wavelength imaging. With i.i.d. standard Gaussian matrices <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A_{i}$</tex-math></inline-formula> , this …