A note on a Matrix Approach to Multiwavelet Applications

In recent years, many papers have been devoted to the topic of balanced multiwavelets, namely, multiwavelet bases which are especially designed to avoid the prefiltering step in the implementation of the multiwavelet transform. In this work, we give a simple algebraic proof of how scalar wavelets can be reinterpreted as the most natural balanced multiwavelets, which maintain the good properties of the wavelet bases they come from. We then show how these new bases can be successfully used to apply matrix thresholding for the denoising of images corrupted by Gaussian noise. In fact, this new approach discovers a balanced matrix nature in Daubechies bases, hence obtaining better numerical results with respect to those achieved via scalar thresholding. In particular, this reinterpretation of scalar wavelets as balanced multiwavelets allows us to successfully use the thresholding filters, previously introduced in the scalar case, in a matrix setting.