Proximal methods for calibration transfer

Calibration transfer (CT) is the process of transferring a calibration curve from one instrument to another or from one set of conditions to another. Direct standardization (DS) of the spectra from a source to a target representation is a popular method of CT, but the multivariate objective function is often significantly underdetermined. Piecewise DS regularizes DS by assuming only local differences between source and target spectra but requires the same wavelength sampling between instruments. In this work, a regularization framework from the field of convex optimization, proximal regularizers, is introduced to standardize instruments that sample at different wavelength ranges and where the differences may have global effects on the spectra. In this framework, penalty terms are appended to the DS objective function to enforce certain behaviors in the transfer matrix and the resulting transferred spectra, including sparsity and smoothness. This framework is shown to be effective at transferring spectra from a source near‐infrared instrument with a narrow wavelength range to a target instrument with a much wider wavelength range. This is demonstrated using two publicly available near‐infrared datasets.