Fast algorithm for quadratic and cubic spline wavelets

We studied the computational complexity of the over-complete wavelet representation for commonly used quadratic and cubic spline wavelets. It is found that the inverse transform is significantly more complicated than the forward transform. In order to reduce the computational complexity, a new spatial implementation is proposed. This spatial implementation is based on exploration of the redundancy between lowpass and bandpass outputs. It is shown that by using the proposed implementation, the computation can be greatly simplified, resulting in an efficient inverse structure