The resolution of radar images is constantly increasing. As a result, radar images require more storage space, which is associated with increased costs. Therefore, it is advantageous to minimize the data size. In this paper, we present various compression methods for reducing the data size of radar images. Compression and decompression are performed in two scenarios. In the first scenario, the raw data are compressed and decompressed before the image is reconstructed. In the second scenario, the reconstructed image itself is compressed and decompressed. In both scenarios, the reconstructed radar image is compared with the original image. Due to its widespread use, High-Efficiency Video Coding (HEVC) is used as a state-of-theart benchmark for both scenarios and compared with proprietary algorithms that combine lossy and lossless compression. A discrete Fourier transform-based compression algorithm from the automotive sector is used as another state-ofthe-art benchmark. This is applied against against our novel approaches, which are based on the discrete cosine transform, use of direct thresholding in the spatial domain, or are applied to the maximum intensity projection. With the exception of HEVC, all algorithms presented have in common that they perform lossy data processing in the first step and then use the Lempel-Ziv-Markov algorithm as a lossless compression step. To compare the compression ratios, we use various image-and video-specific metrics, such as the peak signal-to-noise ratio (PSNR), the similarity of speeded-up robust features, and the structural similarity index measure (SSIM). For a simple classification, we use Otsu's method to examine the effects of compression on the images. The radar images are categorized into transparent and nontransparent based on the measurement objects. Depending on the application and the desired resolution, our approaches can achieve storage savings of up to 99.93 % compared to the uncompressed data with PSNR and SSIM values of 38.8 dB and 0.916, respectively.