System and method for transcoding spectral data with task-based optimization via symmetric non-negative matrix factorization

A computer-implemented method for reconstructing/recovering high-resolution visible light spectral data at a target resolution d, that comprises obtaining a configuration of a low- resolution multi-channel imaging sensor of resolution p, the configuration being enabled to produce measurements results of any one of a plurality of n determined visible light spectra, the low-resolution multi-channel imaging sensor comprising a number p of optical sensors arranged at locations in the spectrometer corresponding each to an attributed measurable wavelength of the visible light, the configuration comprising a definition of the attributed measurable wavelength for each location. The method comprises obtaining a library L comprising a previously measured set of the plurality of n determined visible light spectra at a high-resolution resolution d, the resolution d being greater than the resolution p, constructing a vector of p channel peak wavelengths by determining the first p channels with the highest evenness to maximize encoded information. The method comprises obtaining a set of reference spectra from L by finding the first k cluster centers such that f(H,k) = min(||A- HH'||2) to be used to fit regularization parameters for unknown spectra via Tikhonov regularization and adaptive dictionary learning.