Research on the spectral reconstruction of a low-dimensional filter array micro-spectrometer based on a truncated singular value decomposition-convex optimization algorithm

TL;DR

This paper introduces a high-precision spectral reconstruction algorithm for micro-spectrometers using truncated singular value decomposition and convex optimization, addressing stability and accuracy issues in miniature spectrometer engineering.

Contribution

It proposes a novel spectral reconstruction method combining filter optimization and joint cross-validation, improving stability and accuracy for micro-spectrometer applications.

Findings

Spectral angle cosine value exceeds 0.995 under multiple reconstructions.

Reconstruction accuracy with cosine value above 0.99.

Algorithm demonstrates high stability and precision in spectral reconstruction.

Abstract

Currently, the engineering of miniature spectrometers mainly faces three problems: the mismatch between the number of filters at the front end of the detector and the spectral reconstruction accuracy; the lack of a stable spectral reconstruction algorithm; and the lack of a spectral reconstruction evaluation method suitable for engineering. Therefore, based on 20 sets of filters, this paper classifies and optimizes the filter array by the K-means algorithm and particle swarm algorithm, and obtains the optimal filter combination under different matrix dimensions. Then, the truncated singular value decomposition-convex optimization algorithm is used for high-precision spectral reconstruction, and the detailed spectral reconstruction process of two typical target spectra is described. In terms of spectral evaluation, due to the strong randomness of the target detected during the working process of the spectrometer, the standard value of the target spectrum cannot be obtained. Therefore, for the first time, we adopt the method of joint cross-validation of multiple sets of data for spectral evaluation. The results show that when the random error of positive or negative 2 code values is applied multiple times for reconstruction, the spectral angle cosine value between the reconstructed curves becomes more than 0.995, which proves that the spectral reconstruction under this algorithm has high stability. At the same time, the spectral angle cosine value of the spectral reconstruction curve and the standard curve can reach above 0.99, meaning that it realizes a high-precision spectral reconstruction effect. A high-precision spectral reconstruction algorithm based on truncated singular value-convex optimization, which is suitable for engineering applications, is established in this paper, providing important scientific research value for the engineering application of micro-spectrometers.