Multiwavelet-Like Bases for High Quality Image Interpolation

We present a simple but generalized interpolation method for digital images that uses multiwavelet-like basis functions. Most of interpolation methods uses only one symmetric basis function; for example, standard and shifted piecewise-linear interpolations use the “hat” function only. The proposed method uses q different multiwavelet-like basis functions. The basis functions can be dissymmetric but should preserve the “partition of unity” property for high-quality signal interpolation. The scheme of decomposition and reconstruction of signals by the proposed basis functions can be implemented in a filterbank form using separable IIR implementation. An important property of the proposed scheme is that the prefilters for decomposition can be implemented by FIR filters. Recall that the shifted-linear interpolation requires IIR prefiltering, but we find a new configuration which reaches almost the same quality with the shifted-linear interpolation, while requiring FIR prefiltering only. Moreover, the present basis functions can be explicitly formulated in time-domain, although most of (multi-)wavelets don't have a time-domain formula. We specify an optimum configuration of interpolation parameters for image interpolation, and validate the proposed method by computing PSNR of the difference between multi-rotated images and their original version.