an:02076489
Zbl 1051.65067
Byrne, Charles
A unified treatment of some iterative algorithms in signal processing and image reconstruction
EN
Inverse Probl. 20, No. 1, 103-120 (2004).
00102443
2004
j
65J15 94A08 94A12 47J25 65K05 90C25 65F10
nonlinear operators; signal processing; image reconstruction, bandlimited extrapolation; convex feasibility problem; algorithms; Krasnoselskii-Mann iterative procedure; nonexpansive continuous operators; Hilbert space; Gerchberg-Papoulis method; SART algorithm; Landweber algorithm; variational inequality; monotone operators
The author gives a unified treatment of several well-known algorithms in signal processing and image reconstruction. These are special case of the Krasnoselskii-Mann iterative procedure [cf. \textit{W. R. Mann}, Proc. Am. Math. Soc. 4, 506--510 (1953; Zbl 0050.11603)] to finding fixed points of nonexpansive continuous operators on Hilbert space. They include the Gerchberg-Papoulis method [cf. \textit{A. Papoulis}, IEEE Trans. Circuits and Systems CAS-22, No. 9, 735--742 (1975)] for bandlimited extrapolation, the SART algorithm of \textit{A. Anderson} and \textit{A. Kak} [Simultaneous algebraic reconstruction technique (SART): A superior implementation of the ART algorithm. Ultrason. Imaging 6, 81--94 (1984)], the Landweber and projected Landweber algorithm [cf. \textit{L. Landweber}, Am. J. Math. 73, 615--624 (1951; Zbl 0043.10602)], simultaneous and sequential methods for solvig the convex feasibility problem, the ART and Cimmino methods [cf. \textit{G. Cimmino}, Ric. Sci. Progr. Tecn. Econom. Naz. 1, 326--333 (1938; Zbl 0018.41802)]for solving linear systems of equations, the CQ algorithm for solving the split feasibility problem and \textit{Z. O. Dolidze}'s procedure [Ekonom. i Mat. Metody 18, No. 5, 925--929 (1982)] for the variational inequality problem for monotone operators.
Karel Najzar (Praha)
Zbl 0018.41802; Zbl 0043.10602; Zbl 0050.11603