We propose the application of Compressed Sensing to Computational Scattered Light Imaging to decrease measurement time and data storage. Computational Scattered Light Imaging (ComSLI) determines three-dimensional fiber orientations and crossings in biomedical tissues like brain tissue. Currently, conventional ComSLI is time-consuming and generates large data. Compressed Sensing reconstructs signals with fewer samples than required by the Shannon-Nyquist theorem with minimal perceptual loss, significantly reducing the number of measurements. We introduce an optimized illumination strategy for ComSLI based on the Discrete Cosine Transform and validate it by reconstructing characteristic scattering patterns in vervet brain tissue, thereby demonstrating the feasibility of Compressed Sensing in ComSLI.