On the Instability of Arbitrary Biorthogonal Wavelet Packets
Albert Cohen, Ingrid C. Daubechies · SIAM Journal on Mathematical Analysis · 1993
Starting from a multiresolution analysis and the corresponding orthonormal wavelet basis, Coifman and Meyer have constructed wavelet packets, a library from which many different orthonormal bases can be picked. This paper proves that when the same procedure is applied to biorthogonal wavelet bases, not all the resulting wavelet packets lead to Riesz bases for $L^2 (\mathbb{R})$.