Spectral reconstruction with sparse representation for the imaging spectrometer using broad-bandpass filters

Abstract

Computational spectral imaging technology is an effective method to miniaturize the imaging spectrometer. Stable spectral reconstruction has been achieved with on-chip spectrometers using broad-bandpass filter dot-arrays. The imaging spectrometer using broad-bandpass filter line-arrays is developed for computational spectral imaging. Due to the processing difficulty of actual filter line arrays, 20-line arrays of the broad bandpass filter were selected in the pre-study. The discrete linear model is developed by analyzing the system response of the imaging spectrometer. The sparse constraint is introduced into the current underdetermined solution system to guarantee a unique and accurate solution; since the solution of hyperspectral bands cannot be performed using a small number of filters. The incoherence analysis of the system response and the dictionary is carried out to identify the general orthogonal systems such as the discrete cosine transform (DCT), etc. that can be used as the dictionary. The OMP was used for the final implementation of the simulation to realize the spectral reconstruction in the Visible-NIR. The results of the reconstruction show that the DCT as the dictionary has the highest accuracy: mean square error ≤8.24×10-4. The different accuracy of various spectral reconstructions using different sparse transforms indicates the existence of different sparse transforms with different sensitivity to the detail and the global of the target spectrum.