Evolving wavelet and scaling numbers for optimized image compression: forward, inverse, or both? A comparative study

The 9/7 wavelet is used for a wide variety of image compression tasks. Recent research, however, has established a methodology for using evolutionary computation to evolve wavelet and scaling numbers describing transforms that outperform the 9/7 under lossy conditions, such as those brought about by quantization or thresholding. This paper describes an investigation into which of three possible approaches to transform evolution produces the most effective transforms. The first approach uses an evolved forward transform for compression, but performs reconstruction using the 9/7 inverse transform; the second uses the 9/7 forward transform for compression, but performs reconstruction using an evolved inverse transform; the third uses simultaneously evolved forward and inverse transforms for compression and reconstruction. Three image sets are independently used for training: digital photographs, fingerprints, and satellite images. Results strongly suggest that it is impossible for evolved transforms to substantially improve upon the performance of the 9/7 without evolving the inverse transform.