Research on the Spectral Reconstruction of a Low-Dimensional Filter Array Micro-Spectrometer Based on a Truncated Singular Value Decomposition-Convex Optimization Algorithm

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.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, 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 +/− 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, is established in this paper, providing important scientific research value for the engineering application of micro-spectrometers.