Reconstruction from nonuniform data using the energy reduction, the steepest descent, and the contraction mapping method
Yongwan Park · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
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(jwtn)}, where {tn} are the unevenly spaced sampling points, form a complete set in the signal subspace of the original signal.