Light spectra are a very important source of information for diverse classification problems, e.g., for discrimination of materials. To lower the cost for acquiring this information, multispectral cameras are used. Several techniques exist for estimating light spectra out of multispectral images by exploiting properties about the spectrum. Unfortunately, especially when capturing multispectral videos, the images are heavily affected by noise due to the nature of limited exposure times in videos. Therefore, models that explicitly try to lower the influence of noise on the reconstructed spectrum are highly desirable. Hence, a novel reconstruction algorithm is presented. This novel estimation method is based on the guided filtering technique which preserves basic structures, while using spatial information to reduce the influence of noise. The evaluation based on spectra of natural images reveals that this new technique yields better quantitative and subjective results in noisy scenarios than other state-of-the-art spatial reconstruction methods. Specifically, the proposed algorithm lowers the mean squared error and the spectral angle up to 46% and 35% in noisy scenarios, respectively. Furthermore, it is shown that the proposed reconstruction technique works out-of-the-box and does not need any calibration or training by reconstructing spectra from a real-world multispectral camera with nine channels.