The continuous wavelet transform as a maximum entropy solution of the corresponding inverse problem

The continuous wavelet transform is obtained as a maximum entropy solution of the corresponding inverse problem. It is well known that although a signal can be reconstructed from its wavelet transform, the expansion is not unique due to the redundancy of continuous wavelets. Hence, the inverse problem has no unique solution. If we want to recognize one solution as "optimal", then an appropriate decision criterion has to be adopted. We show here that the continuous wavelet transform is an "optimal" solution in a maximum entropy sense.