Adaptive Quadratic Interpolation Methods for Lifting Steps Construction

An adaptive quadratic method for image interpolation is described. The method is reformulated as an optimization of a quadratic objective function with linear constraints. The proposed formulation is useful for the derivation of new prediction and update lifting steps, which amounts to create new discrete wavelet transforms. The lifting step performance is related to the quadratic interpolation performance. This connection is established and it leads to the proposal of several variations on the initial interpolation formulation. The methods consider possible additional available information and they are suited for different kind of images. The interpolation methods are tested with a set of images in terms of the PSNR. Results are around 1.5-2 dB better than the widespread bicubic interpolation