Tomography with a finite set of projections: Singular value decomposition and resolution

Inverse Problems

Volumn 13, Issue 5, 1997, Pages 1191-1205

  Caponnetto, A ^a   Bertero, M ^a  

^a UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ESTIMATION; FUNCTIONS; INVERSE PROBLEMS; MATHEMATICAL TRANSFORMATIONS; PROJECTION SYSTEMS;

EQUISPACED PROJECTIONS; RADON TRANSFORM; SINGULAR VALUE DECOMPOSITION;

RADIOLOGY;

EID: 0031247452     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/13/5/006     Document Type: Article

References (11)

1. Davison M E 1981 A singular value decomposition for the Radon transform in n-dimensional euclidean space Num. Funct. Anal. Optimiz. 3 321-40
2. Davison M E and Grünbaum F A 1981 Tomographic reconstructions with arbitrary directions Comm. Pure Appl. Math. 34 77-120
3. Logan B F 1975 The uncertainty principle in reconstructing functions from projections Duke Math. J. 42 661-706
4. Louis A K 1984 Orthogonal function series expansions and the null space of the Radon transform SIAM J. Math. Anal. 15 621-33
5. Natterer F 1986 The Mathematics of Computerized Tomography (Stuttgart: Teubner)
6. Kak A C and Slaney M 1988 Principles of Computerized Tomographic Imaging (New York: IEEE)
7. Davison M E 1983 The ill-conditioned nature of the limited angle tomography problem SIAM J. Appl. Math. 43 428-48
8. Louis A K 1986 Incomplete data problems in X-ray computerized tomography Numer. Math. 48 251-62
9. Miller K 1970 Least squares methods for ill-posed problems with a prescribed bound SIAM J. Math. Anal. 1 52-74
10. Logan B F and Shepp L A 1975 Optimal reconstruction of a function from its projections Duke Math. J. 42 645-59
11. Abramovitz M and Stegun I A 1965 Handbook of Mathematical Functions (New York: Dover)