Rational filters are extended to multichannel signal processing and applied to image interpolation. Two commonly used decimation schemes are considered: a rectangular grid and a quincunx grid. For each decimation lattice, we propose a number of adaptive resampling algorithms based on the vector rational filter (VRF). These algorithms exhibit desirable properties such as edge and detail preservation and accurate chromaticity estimation. In these approaches, color image pixels are considered as three-component vectors in the color space. Therefore, the inherent correlation that exists between the different color components is not ignored. This leads to better image quality compared to that obtained by componentwise or marginal processing. Extensive simulations show that multichannel image processing with the proposed algorithms (VRFL) and (VRFd) based on lp-norm and directional processing, respectively; significantly outperform linear and some nonlinear techniques, e.g., vector FIR median hybrid filters (VFMH). Some images interpolated using VRFL and VRFd are presented for qualitative comparison. These images are free from blockiness and jaggedness, confirming the quantitative results.