Compressive Phase Retrieval From Squared Output Measurements Via Semidefinite Programming
2012 (English)In: Proceedings of the 16th IFAC Symposium on System Identification, 2012, 89-94 p.Conference paper (Refereed)
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear program, namely, l1-minimization, guarantees recovery of sparse parameter signals even when the system is underdetermined. In this paper, we consider a more challenging problem: when the phase of the output measurements from a linear system is omitted. Using a lifting technique, we show that even though the phase information is missing, the sparse signal can be recovered exactly by solving a semidefinite program when the sampling rate is sufficiently high. This is an interesting finding since the exact solutions to both sparse signal recovery and phase retrieval are combinatorial. The results extend the type of applications that compressive sensing can be applied to those where only output magnitudes can be observed. We demonstrate the accuracy of the algorithms through extensive simulation and a practical experiment.
Place, publisher, year, edition, pages
2012. 89-94 p.
Phase retrieval, Compressive sensing, Compressive phase retrieval, X-ray crystallography, X-ray diffraction, Lifting, Sparse, Semidefinite programming
IdentifiersURN: urn:nbn:se:liu:diva-88927DOI: 10.3182/20120711-3-BE-2027.00415ISBN: 978-3-902823-06-9OAI: oai:DiVA.org:liu-88927DiVA: diva2:606304
16th IFAC Symposium on System Identification, Brussels, Belgium, 11-13 July, 2012
FunderEU, European Research Council, 267381Linnaeus research environment CADICS