Hyperspectral imaging (HSI) is a powerful tool widely used for various scientific and industrial applications due to its ability to provide rich spatiospectral information. However, in exchange for multiplex spectral information, its image acquisition rate is lower than that of conventional imaging, with up to a few colors. In particular, HSI in the infrared region and using nonlinear optical processes is impractically slow because the three-dimensional (3D) data cube must be scanned in a point-by-point manner. In this study, we demonstrate a framework to improve the spectral image acquisition rate of HSI by integrating time-domain HSI and compressed sensing. Specifically, we simulated broadband coherent Raman imaging at a record high frame rate of 25 frames per second (fps) with 100 pixels × 100 pixels, which is 10 × faster than that of previous work, based on an experimentally feasible sampling scheme utilizing 3D Lissajous scanning.