Biorthogonal two-direction refinable function and two-direction wavelet

The concept of two-direction refinable function and two-direction wavelet is generalized to the biorthogonal setting. The definition of biorthogonal two-direction refinable function is introduced, and the biorthogonality criteria for two-direction refinable function is established. We present an algorithm for constructing a pair of biorthogonal two-direction refinable function and the corresponding biorthogonal two-direction wavelet. Finally, we give two examples illustrating how to use our method to construct a pair of biorthogonal refinable function and its corresponding biorthogonal two-direction wavelet pair.