The application of multiwavelet filterbanks to image processing

Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multi wavelets offer simultaneous orthogonality, symmetry, and short support, which is not poss ible with scalar two-channel wavelet systems. After reviewing this recently developed theory, we examine the use of multiwavelets in a filterbank sett ing for discrete-time signal and image processing, Multiwavelets differ fro m scalar wavelet systems in requiring two or more input streams to the mult iwavelet filterbank, We describe two methods (repeated row and approximatio n/deapproximation) for obtaining such a vector input stream from a one-dime nsional (1-D) signal, Algorithms for symmetric extension of signals at boun daries are then developed, and naturally integrated with approximation-base d preprocessing, We describe an additional algorithm for multiwavelet proce ssing of two-dimensional (2-D) signals, two rows at a time, and develop a n ew family of multiwavelets (the constrained pairs) that is well-suited to t his approach. This suite of novel techniques is then applied to two Basic s ignal processing problems, denoising via wavelet-shrinkage, and data compre ssion, After developing the approach via model problems in one dimension, w e apply multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform.