Using light spectra is an essential element in many applications, for example, in material classification. Often this information is acquired by using a hyperspectral camera. Unfortunately, these cameras have some major disadvantages like not being able to record videos. Therefore, multispectral cameras with wide-band filters are used, which are much cheaper and are often able to capture videos. However, using multispectral cameras requires an additional reconstruction step to yield spectral information. Usually, this reconstruction step has to be done in the presence of imaging noise, which degrades the reconstructed spectra severely. Typically, same or similar pixels are found across the image with the advantage of having independent noise. In contrast to state-of-the-art spectral reconstruction methods which only exploit neighboring pixels by block-based processing, this paper introduces non-local filtering in spectral reconstruction. First, a block-matching procedure finds similar non-local multispectral blocks. Thereafter, the hyperspectral pixels are reconstructed by filtering the matched multispectral pixels collaboratively using a reconstruction Wiener filter. The proposed novel procedure even works under very strong noise. The method is able to lower the spectral angle up to 18% and increase the peak signal-to-noise-ratio up to 1.1dB in noisy scenarios compared to state-of-the-art methods. Moreover, the visual results are much more appealing.