A Hybrid Projection Reflection Method for Phase Retrieval.pdf

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2017-04-13 发布于江苏
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A Hybrid Projection Reflection Method for Phase Retrieval.pdf

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A Hybrid Projection Reflection Method for Phase Retrieval

PIMS-Director director@pims.math.ca (604) 822-3922 SFU-site sfu@pims.math.ca (604) 268-6655 UCalgary-site uc@pims.math.ca (403) 220-3951 UAlberta-site ua@pims.math.ca (780) 492-4308 UVic-site uvic@pims.math.ca (250) 472-4271 UBC-site ubc@pims.math.ca (604) 822-3922 UWashington-site uw@pims.math.ca (206) 543-1173 A Hybrid Projection Reflection Method for Phase Retrieval Heinz H. Bauschke Patrick L. Combettes D. Russell Luke Department of Math. Stats Laboratoire Jacques-Louis Lions PIMS University of Guelph Universite? Pierre et Marie Curie – Paris 6 Simon Fraser University Guelph, ON N1G 2W1, Canada 75005 Paris, France Burnaby, BC V5A 1S6, Canada Preprint number: PIMS-03-2 Received on February 6, 2003 A Hybrid Projection Reflection Method for Phase Retrieval Heinz H. Bauschke Department of Mathematics and Statistics, University of Guelph Guelph, Ontario N1G 2W1, Canada. Patrick L. Combettes Laboratoire Jacques-Louis Lions, Universite? Pierre et Marie Curie – Paris 6 75005 Paris, France. D. Russell Luke The Pacific Institute for the Mathematical Sciences, Simon Fraser University Burnaby, British Columbia V5A 1S6, Canada. February 6, 2003 – version 1.73 Abstract The phase retrieval problem, fundamental in applied physics and engineering, asks to determine the phase of a complex-valued function from modulus data and additional a priori informa- tion. Recently, we identified two important methods for phase retrieval, namely Fienup’s Basic Input-Output (BIO) and Hybrid Input-Output (HIO) algorithms, with classical convex projec- tion methods and suggested that further connections between convex optimization and phase retrieval should be explored. Following up on this work, we introduce a new projection-based method, termed the Hybrid Projection Reflection (HPR) algorithm, for solving phase retrieval problems featuring nonnegativity constraints in the object domain. Motivated by properties of the HPR algorithm for convex constraints, we recommend an error measure studied