Single-sensor digital cameras spatially sample the incoming image using a color filter array (CFA). Consequently, each pixel only contains a single color value. In order to reconstruct the original full-color image, a demosaicing step must be performed which interpolates the missing colors at each pixel. Goals in CFA demosaicing include color fidelity, spatial resolution, no false colors, no jagged edges, and computational practicality. Most demosaicing algorithms do well for color fidelity, but there is often a trade-off between a sharp image and the so-called 'zipper effect' or jagged edge look. We propose a novel demosaicing algorithm called vector demosaicing that interpolates missing colors jointly by selecting the color vector that minimizes the sum of distances to the surrounding pixels. The selected color vector is a vector median of the surrounding pixels. The vector median forms an 'average', but preserves sharp edges. We will discuss the theory behind our approach and show experimentally how the theoretical advantages manifest themselves to improve edge resolution while retaining smoothness. Computational complexity is shown to be possible quite low, and we discuss how different approximations may affect the output.