A Data Driven Correction Algorithm for Inverse Problems with Application to Spectral Reconstruction

Plasmonic filter arrays offer a potential solution for creating compact and cost-effective spectrometers. However, they cannot filter accurately at specific wavelengths, resulting in raw outputs that do not adequately represent the spectra of measured objects. Consequently, a process is required to reconstruct the spectra from the CSS (Chip-Size Spectrometer) values. This paper presents a novel procedure for reconstruction that employs a transformation correction of the measured CSS values before approximating the spectra. The performance of this method is compared with a deep learning architecture, as well as least squares with Tikhonov regularization and Ridge regression. This evaluation is conducted using data from two different plasmonic filter arrays and a set of measurements based on transmittance foils. The results demonstrate that our method outperforms other approaches and achieves better reconstruction accuracy compared to pure learning methods, while needing significantly less data.