A new class of full rank filters in the context of digital color image processing.

Considering that digital color images are the most prominent type of two-dimensional data more powerful and sophisticated algorithms to process these kind of objects are required day by day. Wavelet, multiwavelet and more recently multichannel wavelet schemes have been implemented and developed with important results. In this work we focus on full rank filters. These particular filters satisfy discrete versions of the approximation, zero-moments properties and, consequently, they allow to avoid the pre-filtering of data usually required in a multiwavelet decomposition/reconstruction scheme. We also present a new class of full rank filters with multiplicity r = 3 constructed via Lifiting and Dual Lifting scheme. Their particular structure makes them suitable for a real vector-valued signal analysis so particularly efficient in the context of color images processing. The performance of these full rank filters is tested with a set of digital color test images by means PSNR (Peak Signal to Noise Ratio) and WPSNR (Weight Peak Signal to Noise Ratio) values in the context of compression and denoising problems.