This paper explores hyperspectral reflectance factor estimation using Gaussian process regression with multispectral- and trichromatic measurements. Estimations are performed in visible- (400-700 nm) or visible-near infrared (400-980 nm) wavelength ranges using the learning-based approach, where sensor and light spectral characteristics are not required. We first construct new estimation models via Gaussian processes, show connection to previous kernel-based models, and then evaluate new models by using marginal likelihood optimization within the probabilistic interpretation. By using standard spectral ensembles and several images in experiments, we evaluate new models with anisotropic radial- and combination kernels (process covariance), marginal likelihood optimization (parameter selection), as well as with input data transformations (pre-processing). Several new Gaussian process models provide spectral accuracy improvements for simulated and real data, when compared with the previous kernel-based models. Most versatile new model is using spectral subspace coordinate learning and combination kernels, and can be efficiently optimized via marginal likelihood. Preliminary results suggest that new models provide uncertainty estimates, which can be used for iterative training set augmentation.