In the process of "spectral reconstruction" of quantum dot spectroscopy, the basis function is needed to construct regression model. The traditional reconstruction methods can not capture the high frequency information of the spectrum, and the inversion accuracy is low. To overcome the shortcomings of traditional methods, a special structure of basis function was proposed, to facilitate the fitting of low-frequency macro-contour information and high-frequency micro-detail information of the spectrum to be measured. At the same time, the adjustment mechanism of the parameters of the basis function will also be studied, so that the parameters of the basis function can be adjusted adaptively. Individualized basis functions were customized for each spectrum to maximize the frequency information of the function to be measured. The test results show that the inversion error of this method is about 50%-70% and 90% of the error of the traditional method for narrow-band and broadband spectra, respectively, and it has a certain anti-noise ability, which lays a foundation for the practical application of quantum dot spectroscopy technology.