Phase retrieval of real-valued functions in Sobolev space (Q1633861)

Phase retrieval plays important roles in many applications. This paper firstly shows that up to a global sign, a real-valued function in \(L^2\) Sobolev space \(H^s(\mathbb R^d)\) can be determined by some phaseless measurements. Then the stability for a special type of perturbations is proved for any smooth functions in \(H^s(\mathbb R^d)\); Finally, the authors conclude the uniform convergence of their reconstruction algorithm, when the smooth function in \(H^s(\mathbb R^d)\) satisfies that its Fourier transform is integrable. In addition, numerical experiments verify their theoretic results.