Accelerated Iterative Band-Limited Extrapolation Algorithms

Salomon, Benjamin G.; Ur, Hanoch

doi:10.1109/lsp.2004.836950

Cited by 17 publications

(9 citation statements)

References 15 publications

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“…For inexact data, the reconstruction seems also relatively satisfactory in the sense that the main features of the signal are preserved, as can be seen from Fig.4, while the reconstruction errors measured by (17) are about in the order of 3 10 − for all cases. Hence, the results verify again the robustness of the proposed procedure.…”

Section: Simulation Resultsmentioning

confidence: 72%

“…Listed here in the references are just the representative investigations [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Among the various presented algorithms, the conventional Papoulis-Gerchberg iteration-based algorithms or their versions are usually slowly convergent and some time may also lead to unstable results due to the cumulative arithmetic error or the errors in the data.…”

Section: Introductionmentioning

confidence: 99%

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Reconstructing a Band-limited function Using Empirical Orthogonal Functions

Weng

2006

2006 IEEE Instrumentation and Measurement Technology Conference Proceedings

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A reconstruction procedure for a band-limited function from its samples taken in a finite segment is systematically developed under an a priori assumption of bandwidth. The rationale of the proposed scheme is to expand the known signal segment based on a band-limited basis function set and then to generate a set of empirical orthogonal functions (EOF's) adaptively from the sample values of the band-limited function set. Simulation results indicate that, in addition to the attractive adaptive feature, this scheme also appears to guarantee a smooth result for inexact data, thus suggesting the robustness of the proposed procedure.

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Section: Simulation Resultsmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Reconstructing a Band-limited function Using Empirical Orthogonal Functions

Weng

2006

2006 IEEE Instrumentation and Measurement Technology Conference Proceedings

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“…The P-G and Cadzow's algorithms are usually slowly convergent. Salomon and Ur [24] proposed an accelerated iterative algorithm for both algorithms, based on the findings of the best approximation in appropriate subspaces by using the modified Gram-Schmidt procedure.…”

Section: X-ray Tomographymentioning

confidence: 99%

“…Theorem 4.2 is a more general result. Another finite-step convergence result was proposed by Salomon and Ur [24], based on finding best approximation in appropriate subspaces by using the modified Gram-Schmidt procedure in finite dimension.…”

Section: X-ray Tomographymentioning

confidence: 99%

Landweber scheme for compact operator equation in Hilbert space and its applications

2008

Commun. Numer. Meth. Engng.

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SUMMARYWe study the Landweber scheme for linear compact operator equation in infinite Hilbert spaces. Using the singular value decomposition for compact operators, we obtain a formula for the Landweber scheme after n iterations and iterative truncated error and consequently establish its convergence conditions. Our results extend known results on convergence conditions. As applications, we apply the Landweber scheme to the X-ray tomography and extrapolation of band-limited functions, and establish accelerated strategies for each application.

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“…For this purpose, the Gerchberg-Papoulis (GP) algorithm has been widely used in various problems in signal processing and related fields [2,15,18] . However, when the observed data is corrupted with noise, the GP algorithm is not convergent because the corresponding linear operator is not contractive under the L 2 norm [1] .…”

Section: Introductionmentioning

confidence: 99%