Wavelet synthesis by alternating projections

The coefficients of the quadrature mirror filters involved in orthonormal wavelet or wavelet packets signal decompositions are often chosen in an ad hoc manner. In order to adapt such a decomposition to the signal being analyzed, it may be pertinent to maximize an energy concentration criterion, which leads to a constrained optimization problem. A simple geometric interpretation of this problem is given, and an alternating projection method is proposed to solve it.

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