A Common Formulation for Interpolation, Prediction, and Update Lifting Design

The optimization of a quadratic objective function with linear constraints is useful for interpolation purposes. This formulation may be employed to derive an initial prediction in the lifting scheme domain in order to construct wavelet transforms. We modify the formulation to design final prediction and update lifting steps. The linear constraints relate wavelet bases and coefficients with the underlying signal. The objective function is the detail signal energy for the prediction lifting design and the gradient of the approximation signal for the update. To report concrete results and the power of the approach, we derive update steps using an auto-regressive image model that show better performance than the 5/3 wavelet for the compression of several image classes