Multiresolution pyramid decomposition of images for data compression and transmission have been successfully employed using the common frame of linear subband filtering techniques involving wavelet transform, and Laplacian of Gaussian while multiresolution morphological pyramid decomposition represent a different class of nonlinear filters that maybe used as an optimal predictor of an image. To achieve a desired compression ratio for a specific class of images, a compression algorithm needs to be optimized at all stages from initial mapping to final encoding. We demonstrate the superiority of an optimized wavelet transform based compression algorithm over the standard JPEG from a number of distortion measure criteria for radiographic images. We also describe here a hybrid technique for noisy images where a combination of multiresolution morphological and wavelet filters dramatically reduce the inherent noise and hence increase the peak signal to noise ratio at a particular compression level. Noisy synthetic aperture radar images are chosen as illustrations.