The fast recursive computation of Tchebichef moment and its inverse transform based on Z-transform

The outputs of cascaded digital filters operating as accumulators are combined with a simplified Tchebichef polynomials to form Tchebichef moments (TMs). In this paper, we derive a simplified recurrence relationship to compute Tchebichef polynomials based on Z-transform properties. This paves the way for the implementation of second order digital filter to accelerate the computation of the Tchebichef polynomials. Then, some aspects of digital filter design for image reconstruction from TMs are addressed. The new proposed digital filter structure for reconstruction is based on the 2D convolution between the digital filter outputs used in the computation of the TMs and the impulse response of the proposed digital filter. They operate as difference operators and accordingly act on the transformed image moment sets to reconstruct the original image. Experimental results show that both the proposed algorithms to compute TMs and inverse Tchebichef moments (ITMs) perform better than existing methods in term of computation speed.