A numerical recipe for accurate image reconstruction from discrete orthogonal moments

摘要

Recursive procedures used for sequential calculations of polynomial basis coefficients in discrete orthogonal moments produce unreliable results for high moment orders as a result of error accumulation. This paper demonstrates accurate reconstruction of arbitrary-size images using full-order (orders as large as the image size) Tchebichef and Krawtchouk moments by calculating polynomial coefficients directly from their definition formulas in hypergeometric functions and by creating lookup tables of these coefficients off-line. An arbitrary precision calculator is used to achieve greater numerical range and precision than is possible with software using standard 64-bit IEEE floating-point arithmetic. This reconstruction scheme is content and noise independent.