Nonlinear Unmixing of Hyperspectral Datasets for the Study of Painted Works of Art

Nonlinear unmixing of hyperspectral reflectance data is one of the key problems in quantitative imaging of painted works of art. The approach presented is to interrogate a hyperspectral image cube by first decomposing it into a set of reflectance curves representing pure basis pigments and second to estimate the scattering and absorption coefficients of each pigment in a given pixel to produce estimates of the component fractions. This two‐step algorithm uses a deep neural network to qualitatively identify the constituent pigments in any unknown spectrum and, based on the pigment(s) present and Kubelka–Munk theory to estimate the pigment concentration on a per‐pixel basis. Using hyperspectral data acquired on a set of mock‐up paintings and a well‐characterized illuminated folio from the 15th century, the performance of the proposed algorithm is demonstrated for pigment recognition and quantitative estimation of concentration.