Stable phase retrieval from locally stable and conditionally connected measurements

In this paper, we study the stability of phase retrieval problems via a family locally stable frame measurements in Banach spaces, which call “locally and conditionally connected” (LSCC) measurement schemes. For any signal f space, associate it with weighted graph Gf, defined by LSCC scheme, show that retrievability is determined connectivity Gf. We quantify two common measures connectivity: The Cheeger constant for real-valued signals, algebraic complex-valued signals. then use our results to models. first model, finite-dimensional problem from supported such as windowed Fourier transform. signals “without large holes” are retrievable, Rd grows proportionally d1/2, while Cd d. second model consider an infinite-dimensional shift-invariant space. infinite-dimension even retrievable can have being zero, hence infinite constant. give example monotone polynomial decay has exponential strictly positive