Projected landweber method and preconditioning

Inverse Problems

Volumn 13, Issue 2, 1997, Pages 441-463

  Piana, M ^a   Bertero, M ^a  

^a INFM   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000817395     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/13/2/016     Document Type: Article

References (21)

1. Ivanov V K 1962 On linear problems which are not well-posed Sov. Math. Dokl. 3 981-3
2. Neubauer A 1988 Tikhonov-regularization of ill-posed linear operator equations on closed convex sets J. Approx. Theor. 53 304-20
3. Lagendijk R, Biemond J and Boekee D 1988 Regularized iterative image restoration with ringing reduction IEEE Trans. Acoust. Speech Signal Process. 36 1874-88
4. Eicke B 1992 Iteration methods for convexly constrained ill-posed problems in Hilbert space Num. Funct. Anal. Opt. 13 413
5. Youla D C and Webb H Image restoration by the method of convex projections, Part 1. Theory IEEE Trans. Med. Imaging MI-1 81-94
6. Golub G H and Van Loan C F 1989 Matrix Computations (Baltimore, MD: Johns Hopkins)
7. Strand O N 1974 Theory and methods related to the singular-function expansion and Landweber's iteration for integral equations of the first kind SIAM J. Num. Anal. 11 798
8. Nashed M Z (ed) 1976 Generalized Inverses and Applications (New York: Academic)
9. Youla D C 1987 Mathematical theory of image restoration by the method of convex projections Image Recovery: Theory and Applications (New York: Academic)
10. Bialy H 1959 Iterative behandlung linearer funktionalgleichungen Arch. Rat. Mech. Anal. 4 166-76
11. Vasin V V and Ageev A L 1995 Ill-posed Problems with a priori Information (Utrecht: VSP)
12. Sanz J C and Huang T S 1983 Unified Hubert space approach to iterative least-squares linear signal restoration J. Opt. Soc. Am. 73 1455-65
13. Defrise M and De Mol C 1987 A note on stopping rules for iterative regularization methods and filtered SVD Inverse Problems: An Interdisciplinary Study (Adv. Electr. Electr. Phys., Suppl. 19) ed P C Sabatier (New York: Academic)
14. Gerchberg R W 1974 Super-resolution through error energy reduction Opt. Acta 21 709-20
15. Slepian D 1964 Prolate spheroidal wave functions, Fourier analysis and uncertainty, IV. Extensions to many dimensions, generalized prolate spheroidal functions Bell. Syst. Tech. J. 43 3009-57
16. Bertero M and Pike E R 1982 Resolution in diffraction-limited imaging, a singular value analysis, I. The case of coherent illumination Opt. Acta 29 727-46
17. Donoho D L, Johnstone I M, Hoch J C and Stern A S 1991 Maximum entropy and the nearly black object J R. Stat. Soc. B 54 41-82
18. Gori F 1975 On an iterative method for super-resolution Digest of the International Optical Computing Conf. (Washington, DC, 1975) (IEEE Catalog No 75 CH0941) pp 137-11
19. Slepian D 1967 Restoration of photographs blurred by image motion Bell Syst. Tech. J. 46 2353-62
20. Bertero M, Bindi D, Boccacci P, Cattaneo M, Eva C and Lanza V 1997 Application of the projected Landweber method to the estimation of the source time function in seismology Inverse Problems 13 465-86
21. Fried D L 1995 Analysis of the CLEAN algorithm and implication of superresolution J. Opt. Soc. Am. A 12 853-60