Design of synthesis filter banks for the structural similarity index

The optimal synthesis filter bank (FB) is designed for a given analysis FB by using the structural similarity (SSIM) criteria. Under the assumption that the source signal is a wide sense stationary (WSS) process with known power spectral density (PSD), that the noise is Gaussian white, and that the filter length is equal to the decimation number, the optimization problem is formulated. The closed-form solution is obtained when the mean of the source is zero. It is shown that the optimal FB designed by SSIM criteria and the one by mean square error (MSE) criteria differs only from a scalar factor. Finally, numerical example is given to compare the performance of different synthesis FBs.