Reconstruction from nonuniform data using the energy reduction, the steepest descent, and the contraction mapping method

Yongwan Park

doi:10.1117/12.148612

29 July 1993 Reconstruction from nonuniform data using the energy reduction, the steepest descent, and the contraction mapping method

Yongwan Park

Author Affiliations +

Proceedings Volume 1905, Biomedical Image Processing and Biomedical Visualization; (1993) https://doi.org/10.1117/12.148612
Event: IS&T/SPIE's Symposium on Electronic Imaging: Science and Technology, 1993, San Jose, CA, United States

Abstract

We introduce three iterative methods for reconstructing a band-limited function from its unevenly spaced sampled data. Each iterative method introduces its own varying coefficient which is adaptively determined at each iteration. A varying coefficient for the first algorithm is adaptively determined based on the error energy reduction of the signal. The second method, the method of steepest descent, determines a varying coefficient based on the error energy reduction of the unevenly spaced sampled data. Third, the contraction mapping method determines a varying coefficient based on the distance reduction of the estimated signals. The reconstructed signal from these algorithms converges to the desired signal if the basis functions, {exp(jwt_n)}, where {t_n} are the unevenly spaced sampling points, form a complete set in the signal subspace of the original signal.

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Yongwan Park "Reconstruction from nonuniform data using the energy reduction, the steepest descent, and the contraction mapping method", Proc. SPIE 1905, Biomedical Image Processing and Biomedical Visualization, (29 July 1993); https://doi.org/10.1117/12.148612

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