Projection minimization techniques for orthogonal QMF filters with vanishing moments

In many applications, a cost function is available that determines how "good" the filters of a filter bank decomposition are at performing a particular job. For example, in signal compression, the filters of a quadrature mirror filter (QMF) bank could be rated on their accuracy in compression and reconstruction of a given input signal. Given a cost function and the constraint set, it would be useful to be able to use an iterative minimization algorithm, e.g., steepest descent, to minimize the cost function while satisfying all of the constraints. The resulting performance would exceed an implementation that was not application specific (i.e., fixed filters). A projection minimization approach is taken with the particulars of this application determining the projection space. A constrained conjugate gradient descent approach is taken in choosing a filter pair that minimizes a cost function, but the methodology could be easily modified and applied to a wide variety of iterative minimization techniques.<>