Can we recover a complex signal from its Fourier magnitudes? More generally,
given a set of $m$ measurements, $y_k = |\mathbf a_k^* \mathbf x|$ for $k = 1,
\dots, m$, is it possible to recover $\mathbf x \in \mathbb{C}^n$ (i.e.,
length-$n$ complex vector)? This **generalized phase retrieval