Phase retrieval of evolving signals from space-time samples

Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function x in a Hilbert space ℋ from the absolute values of linear measurements {|〈x, φ
i
〉|, …, |〈A
^Li−1
x, φ
i
〉| ∶ i ∈ ℐ}, where { φ
i
; i ∈ ℐ} ⊂ ℋ is a set of functionals on ℋ, and A is a bounded operator on ℋ that acts as an evolution operator. In this paper, we study this problem in the finite dimensional scenario, and when ℋ is a real Hilbert space.