To address the miniaturization of the spectral imaging system required by a mounted platform and to overcome the low luminous flux caused by current spectroscopic technology, we propose a method for the multichannel measurement of spectra using a broadband filter in this work. The broadband filter is placed in front of a lens, and the spectral absorption characteristics of the broadband filter are used to achieve the modulation of the incident spectrum of the detection target and to establish a mathematical model for the detection of the target. The spectral and spatial information of the target can be obtained by acquiring data using a push-broom method and reconstructing the spectrum using the GCV-based Tikhonov regularization algorithm. In this work, we compare the accuracy of the reconstructed spectra using the least-squares method and the Tikhonov algorithm based on the L-curve. The effect of errors in the spectral modulation function on the accuracy of the reconstructed spectra is analyzed. We also analyze the effect of the number of overdetermined equations on the accuracy of the reconstructed spectra and consider the effect of detector noise on the spectral recovery. A comparison between the known data cubes and our simulation results shows that the spectral image quality based on broadband filter reduction is better, which validates the feasibility of the method. The proposed method of combining broadband filter-based spectroscopy with a panchromatic imaging process for measurement modulation rather than spectroscopic modulation provides a new approach to spectral imaging.