We propose a new efficient method for the design of orthogonal and biorthogonal lapped transforms for image coding applications. It is shown how perception related constraints such as decay and smoothness of the filters' impulse responses can be incorporated in the optimization procedure. A decomposition of lapped transforms (orthogonal and biorthogonal) with 50% overlap leads to an efficient recursive optimization procedure, which is robust with respect to initial solutions. The importance of this decomposition lies in the fact that it allows to decouple the design of the even-symmetric and the odd-symmetric filters and hence drastically reduces the number of variables to be optimized. It furthermore reveals all the variables predetermined by perception related and coding-efficiency related constraints imposed on the filters. We present design and coding examples demonstrating the perceptual performance and the rate distortion performance of the resulting transforms.

The decomposition (analysis) of a finite-energy signal into a relatively small number of mutually independent signals which allows reconstruction (synthesis) of the original signal is called subband filtering. Subbands can be processed in parallel or recursively. In the latter case, one obtains a so-called quadrature mirror filter tree. The former case leads to cosine-modulated filter banks. The authors present a Cordic based cosine-modulated bank and a systolic algorithm for quadrature mirror tree filtering.>