Spring 2014: Research-Interaction-Team on the Phaseless Reconstruction Problem
- Email: rvbalan at math.umd.edu
- Office: Math building 2308 ; Phone: 301 405 5492
- Office: CSCAMM (CSIC building) 4131 ; Phone: 301 405 1217
- Email: kasso at math.umd.edu
Meetings: 2.00pm-3.00pm on Mondays in
This RIT focuses on nonlinear inverse problems. In particular we study results
for the following setup: alpha:H->R^m where (alpha(x))_k = |(Ax)_k| is the absolute value computed entrywise of a linear transform. This problem has applications to X-Ray chrystallography, signal processing, communications, and machine learning, to name a few.
Spring 2014: Finite Dimensional Case
 Jameson Cahill, Peter G. Casazza, Jesse Peterson and Lindsay Woodland, Phase Retrieval by Projections, arXiv:1305.6226v3[math.FA], 18 July 2013.
 Yang Wang, Zhiqiang Xu, Phase Retrieval for Sparse Signals,
arXiv:1310.0873v2[cs.IT], 4 Oct. 2013.
 James Milgram,Immersing Projective Spaces, Annals Mathematics, vol. 85, no. 3 (1967), 473--482.
 Radu Balan, Stability of Phase Retrievable Frames, arXiv:1308.5465v1[math.FA], 25 Aug. 2013.
 Radu Balan, Dongmian Zou, Phase Retrieval using Lipschitz Continuous Maps, arXiv:1403.2301 [math.FA], 11 Mar. 2014,
1. Convex Optimization
 Emmanuel J. Candes, Thomas Strohmer, Vladislav Voroninski, PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming, Comm.PureAppl.Math., vol. 66, (2013) 1241-1274.
 Laurent Demanet, Paul Hand, Stable optimizationless recovery from phaseless linear measurements, arXiv:1208.1893v2[math.NA], 21 Aug. 2012.
 Emmanuel Candes, Xiaodong Li, Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns, arXiv:1208.6247v2[cs.IT], 17 Sept. 2012.
 Henrik Ohlsson, Allen Y. Yang, Roy Dong, S. Shankar Sastry, CPRL – An Extension of Compressive Sensing to the Phase Retrieval Problem, NIPS 2012.
 Emmanuel J. Candes, Xiaodong Li, Mahdi Soltanolkotabi, Phase Retrieval from Coded Diffraction Patterns, arXiv:1310.3240v2[cs.IT], 6 Nov. 2013.
2. Iterative Methods
 Afonso S. Bandeira and Dustin G. Mixon, Near-Optimal Phase Retrieval of Sparse Vectors,
arXiv:1308.0143v1[cs.IT], 1 Aug. 2013.
 Matthew Fickus, Dustin G. Mixon, Aaron A. Nelson, Yang Wang, Phase retrieval from very few measurements, arXiv:1307.7176v1[math.FA], 26 July 2013.
 Bernhard G. Bodmann and Nathaniel Hammen, Stable Phase Retrieval With Low-Redundancy Frames, arXiv:1302.5487v1[math.FA], 22 Feb 2013.
Fourier Transform case: X-Ray
 Albert Fannjiang, Absolute Uniqueness Of Phase Retrieval With Random Illumination,
Inverse Problems, 28 (2012).
 Albert Fannjiang, Wenjing Liao, Compressed Sensing Phase Retrieval, ASILOMAR 2011
Schedule (all meetings in MATH 0104 at 2:00pm, unless otherwise said):
February 3, 2014: Organizatorial Meeting; Radu Balan: Real Case - the necessary and sufficient condition; 2n-1 result
February 10, 2014: Radu Balan, The complex case (I): Notations: C^n -> R^2n scalar product transfer; sets of symmetric matrices, Sym(H) and S^p,q(H).
February 17, 2014: Radu Balan, The complex case (II): Necessary and Sufficient conditions in terms of R(x) matrix;
February 28, 2014: -- Radu Balan, The complex case (III) - stability bounds as in ;
March 3, 2014:
Xuemei Chen: PhaseLift Algorithm from  (I) canceled: University was closed due to snow
March 14, 2014: Xuemei Chen: PhaseLift Algorithm from  (I) -- NOTE CHANGE OF DAY
March 17, 2014: No meeting (spring break)
March 24, 2014: Xuemei Chen: PhaseLift Algorithm from  (II)
March 31, 2014: Max Scharrenbroich: PhaseLift Algorithm with low redundancy  (I)
April 7, 2014: No meeting
April 14, 2014: Max Scharrenbroich: PhaseLift Algorithm with low redundancy  (II)
April 21, 2014: Ming Zhong: Phase Retrieval for Sparse Signals  (I)
April 28, 2014: Ming Zhong: Phase Retrieval for Sparse Signals  (II)
May 5, 2014: Dongmian Zou: Lipschitz Constant in Phaseless Reconstruction 
May 12, 2014: