Analysis for the reconstruction of a noisy signal based on orthogonal moments

Suppose that we have a set of discrete data of a noisy signal and we reconstruct the original signal from its orthogonal moments based on Legendre polynomials. In this paper we derive a new error estimation of the reconstruction, which reveals the relationships between the number of moments, the signal smoothness and sampling rate. Numerical simulations provided are consistent with our analysis.

[1]  G. Talenti.  Recovering a function from a finite number of moments , 1987 .

[2]  D. Gottlieb,et al.  Numerical analysis of spectral methods : theory and applications , 1977 .

[3]  J. F. Boyce,et al.  Moment invariants for pattern recognition , 1983, Pattern Recognit. Lett..

[4]  Miroslaw Pawlak,et al.  On the reconstruction aspects of moment descriptors , 1992, IEEE Trans. Inf. Theory.

[5]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[6]  Roland T. Chin,et al.  On Image Analysis by the Methods of Moments , 1988, IEEE Trans. Pattern Anal. Mach. Intell..