1. A method to control a quality of one or more of an image, a sequence of images, a video sequence, a 3-dimensional data set and a layer of an image comprising: receiving, by an image receipt module, the one or more of the image, the sequence of images, the video sequence, the 3-dimensional data set and the layer of the image; receiving, by a compression module, a quality metric for a target image quality for a reconstructed version of a to be compressed version of the one or more of the image, the sequence of images, the video sequence, the 3-dimensional data set and the layer of the image; commencing compression, using the compression module and memory, of the one or more of the image, the sequence of images, the video sequence, the 3-dimensional data set and the layer of the image, the compression including performing a wavelet transform and a wavelet coefficient coding; estimating, using one or more of Laplacian, generalized Gaussian, statistical and empirical modeling, distortion caused by one or more of quantization distortion and truncation distortion, wherein the estimating of distortion is performed without measuring the distortion; estimating, using one or more modeling techniques, a quality of the reconstructed version of the one or more of the image, the sequence of images, the video sequence, the 3-dimensional data set and the layer of the image based on the estimated distortion; automatically comparing, by a processor, the estimated quality to the target image quality; and: when the target image quality has been met, automatically outputting the compressed version of the one or more of the image, the sequence of images, the video sequence, the 3-dimensional data set and the layer of an image that at least meets the target image quality, and when the target image quality has not been met, automatically adjusting one or more of quantization tables and truncation points and re-executing the compressing, estimating, and comparing steps until the target image quality has been met.