A special class of orthonormal wavelets: theory, implementations, and applications

This paper introduces anovel class of length-4N orthonormal scalar wavelets, and presents the theory, implementational issues, and their applications to image compression. We first give the necessary and sufficient conditions for the existence of this class. The parameterized representation of filters with different lengths are then given. Next, we derive new and efficient decomposition and reconstruction algorithms specifically tailored to this class of wavelets. We will show that the proposed discrete wavelet transformations are orthogonal and have lower computational complexity than conventional octave-bandwidth transforms using Daubechies' orthogonal filters of equal length. In addition, we also verify that symmetric boundary extensions can be applied. Finally, our image compression results further confirm that improved performance can be achieved with lower computational cost.