Abstract：Aiming at the problem of a large amount of spectral data and low reconstruction accuracy in the field of spectral reconstruction, a spectral tunable spectral reconstruction method is proposed. Prior to this, domestic and foreign-related research were carried out based on hundreds of film systems, and the calculation process was relatively complicated. This method uses 10 film systems to conduct experiments against different monochromatic light sources and perform the spectral reconstruction. Linear equations can express the mathematical model of spectral reconstruction. During the experiment, it will be interfered with by various error sources, such as the error between film processing and design, the fitting error of the detector quantum efficiency, the stray light interference error, the error of grey value selection, etc. These error sources cause the linear equations to become ill-conditioned equations, resulting in an inaccurate solution of the target spectrum information. In calculating the target spectral information, firstly, the convex optimization algorithm is used to solve the initial value of the target spectral information with errors in the wavelength range of 400~900 nm, and the initial fitting is performed to obtain the spectral curve with errors. Then use the known spectral curve information to determine the effective wavelength range of the target spectrum, expand and contract the target spectral range, perform a secondary local calculation in this range, and obtain the spectral information within the local wavelength. Then the local spectral information is locally fitted, combined with the initial fitting results, and a new target spectral fitting curve is obtained, which further improves the accuracy of the spectral reconstruction and obtains a higher-precision target spectral curve. The evaluation index for reconstruction accuracy not only adopts the widely used ARE, MSE and RQE at home and abroad but also proposes a new index for evaluating the accuracy of spectral reconstruction for the first time, which is to calculate the MSE value every 10 nm within the effective wavelength range of the target. If the MSE value per 10 nm is less than 0.1, the spectrum reconstruction accuracy is considered to have reached 10 nm. This method effectively avoids the serious deviation from the true value in the solution and provides constraint conditions during the convex optimization solution process, which is beneficial to improving the reconstruction accuracy. Experimental results show that this method can achieve a minimum MSE of 0.002 3 every 10 nm under the condition of ensuring high accuracy of MSE, ARE and RQE. The tunable spectrum reconstruction method based on spectrum achieves the effect of high-precision reconstruction of the target spectrum and achieves data dimensionality reduction. This method provides a new idea for the work direction in spectral reconstruction and has great application value in engineering.
Key words：Spectral reconstruction; Tuning spectrum; Convex optimization; Data dimensionality reduction
