Publications [#332858] of Ingrid Daubechies

Papers Published

1. Alaifari, R; Daubechies, I; Grohs, P; Thakur, G, Reconstructing Real-Valued Functions from Unsigned Coefficients with Respect to Wavelet and Other Frames, Journal of Fourier Analysis and Applications, vol. 23 no. 6 (December, 2017), pp. 1480-1494 [doi]
   (last updated on 2025/04/04)

   Abstract:
   In this paper we consider the following problem of phase retrieval: given a collection of real-valued band-limited functions {ψλ}L2(Rd) that constitutes a semi-discrete frame, we ask whether any real-valued function f∈ L2(Rd) can be uniquely recovered from its unsigned convolutions { | f∗ ψλ| } λ∈Λ. We find that under some mild assumptions on the semi-discrete frame and if f has exponential decay at ∞, it suffices to know | f∗ ψλ| on suitably fine lattices to uniquely determine f (up to a global sign factor). We further establish a local stability property of our reconstruction problem. Finally, for two concrete examples of a (discrete) frame of L2(Rd) , d= 1 , 2 , we show that through sufficient oversampling one obtains a frame such that any real-valued function with exponential decay can be uniquely recovered from its unsigned frame coefficients.