RGB to Hyperspectral Image Conversion

Ben Gurion University, Israel, researches implement a physically impossible thing - converting regular RGB consumer camera images into hyperspectral ones, purely by software. Their paper "Sparse Recovery of Hyperspectral Signal from Natural RGB Images" by Boaz Arad and Ohad Ben-Shahar presented at European Conference on Computer Vision (ECCV) in Amsterdam, The Netherlands, in October 2016, says:

"We present a low cost and fast method to recover high quality hyperspectral images directly from RGB. Our approach first leverages hyperspectral prior in order to create a sparse dictionary of hyperspectral signatures and their corresponding RGB projections. Describing novel RGB images via the latter then facilitates reconstruction of the hyperspectral image via the former. A novel, larger-than-ever database of hyperspectral images serves as a hyperspectral prior. This database further allows for evaluation of our methodology at an unprecedented scale, and is provided for the benefit of the research community. Our approach is fast, accurate, and provides high resolution hyperspectral cubes despite using RGB-only input."

"The goal of our research is the reconstruction of the hyperspectral data from natural images from their (single) RGB image. Prima facie, this appears a futile task. Spectral signatures, even in compact subsets of the spectrum, are very high (and in the theoretical continuum, infinite) dimensional objects while RGB signals are three dimensional. The back-projection from RGB to hyperspectral is thus severely underconstrained and reversal of the many-to-one mapping performed by the eye or the RGB camera is rather unlikely. This problem is perhaps expressed best by what is known as metamerism – the phenomenon of lights that elicit the same response from the sensory system but having different power distributions over the sensed spectral segment.

Given this, can one hope to obtain good approximations of hyperspectral signals from RGB data only? We argue that under certain conditions this otherwise ill-posed transformation is indeed possible; First, it is needed that the set of hyperspectral signals that the sensory system can ever encounter is confined to a relatively low dimensional manifold within the high or even infinite-dimensional space of all hyperspectral signals. Second, it is required that the frequency of metamers within this low dimensional manifold is relatively low. If both conditions hold, the response of the RGB sensor may in fact reveal much more on the spectral signature than first appears and the mapping from the latter to the former may be achievable.

Interestingly enough, the relative frequency of metameric pairs in natural scenes has been found to be as low as 10^−6 to 10^−4. This very low rate suggests that at least in this domain spectra that are different enough produce distinct sensor responses with high probability.

The eventual goal of our research is the ability to turn consumer grade RGB cameras into a hyperspectral acquisition devices, thus permitting truly low cost and fast HISs."