Fast algorithms for signal reconstruction without phase

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 6701, Issue , 2007, Pages

  Balan, Radu ^a   Bodmann, Bernhard G ^b   Casazza, Peter G ^c   Edidin, Dan ^c  

^a Bldg 142   (United States)

^b University of Houston   (United States)

^c UNIVERSITY OF MISSOURI   (United States)

Author keywords

Discrete chirps; Equiangular frames; Frames; Mutually unbiased bases; Projective 2 designs

Indexed keywords

ALGORITHMS; POLYNOMIALS; QUANTUM THEORY; SPEECH RECOGNITION; TOMOGRAPHY;

DISCRETE CHIRPS; EQUIANGULAR FRAMES;

SIGNAL RECONSTRUCTION;

EID: 42149168142     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.731117     Document Type: Conference Paper

References (36)

1. R. Balan. Equivalence relations and distances between Hilbert frames. Proc. Amer. Math. Soc., 127(8):2353-2366, 1999.
2. R. Balan, B. G. Bodman, P. G. Casazza and D. Edidin, Painless reconstruction from magnitudes of frame coefficients, preprint.
3. R. Balan, P. Casazza, D. Edidin, On signal reconstruction without phase, Appl.Comput.Harmon.Anal. 20 (2006), 345-356.
4. R. Balan, P. Casazza, D. Edidin, Equivalence of Reconstruction from the Absolute Value of the Frame Coefficients to a Sparse Representation Problem, to appear in IEEE Signal Proc. Letters (2007).
5. R. H. Bates and D. Mnyama. The status of practical Fourier phase retrieval, in W. H. Hawkes, ed., Advances in Electronics and Electron Physics, 67:1-64, 1986.
6. C. Becchetti and L. P. Ricotti. Speech recognition theory and C++ implementation. Wiley (1999).
7. B. G. Bodmann, Optimal linear transmission by loss-insensitive packet encoding, Appl. Comput. Harmon. Anal. 22 (2007), 274-285.
8. B. G. Bodmann and V. I. Paulsen, Frames, graphs and erasures, Linear Algebra Appl. 404 (2005), 118-146.
9. 4-Kerdock codes, orthogonal spreads, and extremal Euclidean line-sets, Proc. London Math. Soc. (3) 75 (1997), no. 2, 436-480.
10. P. J. Cameron and J. J. Seidel, Quadratic forms overGF(2), Indag. Math. 35 (1973), 1-8.
11. P. G. Casazza and M. Fickus, Fourier transforms of finite chirps, EURASIP J. Appl. Signal Process. (2006), Frames and overcomplete representations in signal processing, communications, and information theory, Art. ID 70204, 1-7.
12. P. G. Casazza and G. Kutyniok, Frames of subspaces, Wavelets, frames and operator theory, Contemp. Math., vol. 345, Amer. Math. Soc., Providence, RI, 2004, pp. 87-113.
13. P. G. Casazza and G. Kutyniok, Robustness of fusion frames under erasures of subspaces and of local frame vectors, Contemporary Math (to appear).
14. P. G. Casazza, G. Kutyniok and S. Li, Fusion frames and distributed processing, preprint.
15. P. Casazza and J. Kovačevic̀, Equal-norm tight frames with erasures, Adv. Comp. Math. 18 (2003), 387-430.
16. O. Christensen, An Introduction to Frames and Riesz Bases, Birkhäuser, Boston, 2003.
17. P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), no. 3, 363-388.
18. J. R. Fienup. Reconstruction of an object from the modulus of its fourier transform, Optics Letters, 3 (1978), 27-29.
19. J. R. Fienup. Phase retrieval algorithms: A comparison, Applied Optics, 21 (15) (1982), 2758-2768.
20. V. K. Goyal, J. Kovačevic̀, and J. A. Kelner, Quantized frame expansions with erasures, Appl. Comp. Harm. Anal. 10 (2001), 203-233.
21. D. Han and D. Larson. Frames, bases and group representations, Memoirs American Math. Soc. 147 (2000), no. 697.
22. M. H. Hayes. The reconstruction of a multidimensional sequence from the phase or magnitude of its fourier transform. IEEE Trans. ASSP, 30 (2) (1982), 140-154.
23. R. Holmes and V. I. Paulsen, Optimal frames for erasures, Lin. Alg. Appl. 377 (2004), 31-51.
24. S. D. Howard, A. R. Calderbank, and W. Moran, The finite Heisenberg-Weyl groups in radar and communications, EURASIP J. Appl. Signal Process. (2006), no. Frames and overcomplete representations in signal processing, communications, and information theory, Art. ID 85685, 1-12.
25. A. Klappenecker and M. Rötteler, Mutually unbiased bases are complex projective 2-designs, Proc. Int. Symp. on Inf. Theory, IEEE, 2005, pp. 1740-1744.
26. J. Kovačevic̀, P. L. Dragotti, and V. K. Goyal, Filter bank frame expansions with erasures, IEEE Trans. Inform. Theory 48 (2002), 1439-1450.
27. G. Liu. Fourier phase retrieval algorithm with noise constraints, Signal Processing, 21(4):339-347, 1990.
28. A. Peres, Quantum Theory: Concepts and Methods, Kluwer, Dordrecht, 1993.
29. J.G. Proakis. Algorithms for statistical signal processing. Prentice Hall (2002).
30. J. G. Proakis, J. R. Deller and J. H. L. Hansen. Discrete-Time processing of speech signals. IEEE Press (2000).
31. J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, Symmetric Informationally Complete Quantum Measurements, J. Math. Phys., vol. 45, pp. 2171-2180, 2004.
32. L. Rabiner and B. H. Juang. Fundamentals of speech recognition. Prentice Hall Signal Processing Series (1993).
33. R. F. Streater and A. S. Wightman. PCT, Spin and Statistics and All That. Princeton University Press, Landmarks in Mathematics and Physics, 2000.
34. M. Strauss, Private communication.
35. S. V. Vaseghi. Advanced digital signal processing and noise reduction. Wiley (2002).
36. F. W. Warner. Foundations of differential manifolds and Lie groups Graduate Texts in Mathematics 94. Springer-Verlag 1983.