Optimum filter design for thea trous algorithm

Thea trous algorithm is an efficient method to compute the continuous wavelet transform at dyadic scale. It consists of a bandpass and a lowpass filter. The bandpass filter is the dilated by two mother wavelet samples and the lowpass filter is a trous. The computation accuracy of the algorithm is dependent on the choice of the lowpass filter. This paper derives a closed-form solution for the lowpass filter that minimizes the error bound between the algorithm output and the true transform coefficients. Simulation results show that the improvement over the Lagrange interpolator, commonly used as the lowpass filter, is substantial.