Phase retrieval from the norms of affine transformations

In this paper, we consider the generalized phase retrieval from affine measurements. This problem aims to recover signals x ∈ F d magnitude of transformations y j = ‖ M ⁎ + b 2 , 1 … m where × r { R C } and call it . We first develop a framework for with presenting several necessary sufficient conditions ( ) having property. Next, focus on minimal measurement number establish some results it. Particularly, show if ⊂ has property, then ≥ ⌊ / ⌋ ). also that lower bounds are tight provided | These imply one can reduce by raising i.e. rank highlights notable difference between retrieval. Furthermore, using tools algebraic geometry, (resp. 4 − generic measurements A have property