Adaptive wavelet system for image representation

Adapting wavelet systems to their input signals appears to be a viable option to improving the performance of current wavelet image representation We study the problem of computing an image based optimal wavelet basis with compact support for image representation and provide a general algorithm for computing the optimal wavelet basis. We parameterize the mother wavelet and scaling function of wavelet systems through a set of real coefficients of the relevant quadrature mirror filter (QMF) banks. We then introduce entropy cost as an information measure to describe the distance between a given digital image and its projection into the subspace spanned by the wavelet basis. The optimal basis for the given image is obtained through minimizing this information measure. The resulting subspace is used for image analysis and synthesis. Experiments on medical images show improved compression ratios due to the adaptation of the optimal wavelet basis and demonstrate the potential applications of our methodology in image compression.