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Despite intensive research being conducted on the topic of adaptive filter design in general, adaptive filter design in the discrete wavelet transform (DWT) domain with specific constraints is still an active research area. We have developed a method for the design of a 2-channel perfect-reconstruction adaptive wavelet filter which is optimized under minimum energy constraints in specific bands. The optimal 2-channel conjugate quadrature filter (CQF) bank has been designed using sequential quadratic programming techniques for nonlinear, nonconvex functions in general, although finding a global minimum is not guaranteed. However, such a filter can be effectively used with a wavelet based image encoder for high fidelity transmission of large image data sets at low bit rates.