Generalised information theory for inverse problems in signal processing

IEE Proceedings F: Communications Radar and Signal Processing

Volumn 131, Issue 6, 1984, Pages 660-667

  Pike, E R ^a   McWhirter, J G ^a   Bertero, M ^b   de Mol, C ^c  

^a DEFENCE SCIENCE AND TECHNOLOGY LABORATORY   (United Kingdom)

^b UNIVERSITY OF GENOA   (Italy)

^c UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

INFORMATION THEORY;

SIGNAL PROCESSING;

EID: 0021513269     PISSN: 01437070     EISSN: None     Source Type: Journal    
DOI: 10.1049/ip-f-1.1984.0100     Document Type: Article

References (23)

1. TWOMEY, S.: J. Franklin Inst., 1965, 279, pp. 95-109
2. BERTERO, M., DE MOL, G, and VIANO, G.A.: ‘The stability of inverse problems’ in BALTES, H.P. (Ed.): ‘Inverse scattering problems in optics-Topics in current Physics—Vol. 20’ (Springer, 1980), pp. 161-214
3. SLEPIAN, D., and POLLAK, H.O.: ‘Prolate spheroidal wave functions, Fourier analysis and uncertainty—I’, Bell Syst. Tech. J., 1961, 40, pp. 43-63
4. BHRTERO, M., DE MOL, C, PIKE, E.R., and WALKER, J.: ‘Resolution in diffraction-limited imaging, a singular value analysis IV’, Opt. Ada, (in press)
5. OSTROWSKY, N., SORNETTE, D., PARKER, P., and PIKE, E.R.: ‘Exponential sampling method for light scattering polydispersity analysis’, Opt. Ada, 1981, 28, pp. 1059-1070
6. MCWHIRTER, J., and PIKE, E.R.: ‘On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind’, J. Phys. A, 1978, II, pp. 1729-1745
7. BERTERO, M., BOCCACCI, P., and PIKE, E.R.: ‘On the recovery and resolution of exponential relaxation rates from experimental data: a singular-value analysis of the Laplace transform inversion in the presence of noise’, Proc. R. Soc. London Ser. A, 1982, A383, pp. 15 29
8. SMITHIES, F.: ‘Integral equations’ (Cambridge University Press, 1958)
9. PICARD, E., MAT PALERMO, R.C.: 1910, 29, pp. 615-619
10. HILLE, E., and TAMARKIN, J.D.: Ada Math, 1931, 57, pp. 1-76
11. HAMMERLIN, G., and SCHUMAKER, L.L.: ‘Procedures for kernel approximation and solution of Fredholm integral equations of the second kind’, Numer. Math., 1980, 34, pp. 125-141
12. RALSTON, A.: ‘A first course in numerical analysis’ (McGraw Hill, 1965)
13. WILKINSON, J.H.: ‘The algebraic eigenvalue problem’ (Clarendon Press, Oxford, 1965)
14. BERTERO, M., and PIKE, E.R.: ‘Resolution in diffraction-limited imaging, a singular value analysis. I: The case of coherent illumination’, Opt. Ada., 1982, 29, pp. 727-746
15. BERTERO, M., BOCCACCI, P., and PIKE, E.R.: ‘Resolution in diffraction-limited imaging, a singular value analysis II. The case of incoherent illumination’, Opt. Ada., 1982, 29, pp. 1599-1611
16. BERTERO, M., BOCCACCI, P., and PIKE, E.R.: ‘On the recovery and resolution of exponential relaxation rates from experimental data II’, Proc. R. Soc. London, 1984, A393, pp. 51-65
17. ZHOU, Y, RUSHFORD, C.K., and FROST, R.L.: ‘Singular value decomposition, singular vectors and the discrete prolate spheroidal sequences’, Proc. 1CASSP, 1984, pp. 37.6.1-37.6.4
18. RIESZ, F., and NAGY, B.: ‘Functional analysis’ (New York: Ungar, 1955)
19. BERTERO, M., BRIANZI, P., and PIKE, E.R.: ‘On the recovery and resolution of exponential relaxation rates from experimental data IIP, submitted to Proc. R. Soc. A
20. BERTERO, M., BRIANZI, P., PARKER, P., and PIKE, E.R.: ‘Resolution in diffraction-limited imaging, a singular value analysis III. The effect of staggering and truncation of the data’, Opt. Ada., 1984, 31, pp. 181-201
21. BERTERO, M., and PIKE, E.R.: ‘Particle size distributions from Fraunhofer diffraction I’, Opt. Ada., 1983, 30, pp. 1043-1049
22. BERTERO, M., and PIKE, E.R.: ‘Particle size distributions for Fraunhofer diffraction II—the singular value spectrum’, Opt. Ada., (to be published)
23. BERTERO, M., BRIANZI, P., PIKE, E.R., DE VILLIERS, G.D., OSTROWSKY, N., and LAN, K.: ‘Light scattering polydispersity analysis of molecular diffusion by Laplace transform inversion in weighted spaces’, J. Chem. Phys. Lett., (to be published)