Multiwavelet

A multiwavelet is a vector-valued wavelet with matrix-valued low- pass and band-pass filters , which processes several signals combined as a vector at the same time.

A multiwavelet always has more degrees of freedom than a normal (so-called scalar) wavelet and consequently it can have more properties at the same time. Multiwavelets can be symmetrical , orthogonal and continuous at the same time and have a finite carrier, which is impossible with scalar wavelets with the usual scaling factor of 2.

In order to process scalar signals such as functions or number sequences with the multiwavelet transformation, these must be converted into vector-valued sequences in a preprocessing. This step is justified by the functional analytical interpretation, the multi-scale analysis . If this step is neglected, as is the case with scalar wavelets, unwanted disturbances can occur during processing.

So far, however, there are no convincing examples of multiwavelet transformations for the most well-known application, image compression , which deliver a better result than, for example, the scalar, symmetric, continuous and biorthogonal Daubechies 9/7 wavelet .