A reversible non-multiplying integer time domain lapped transform was introduced, and a new progressive lossy-to-lossless compression system was designed based on this transform technique. Completely lossless compression images and high-quality lossy reconstructed images could be obtained from a single code-stream using the proposed compression system. RTDLT improved the transform efficiency of DCT by adding pre-and-post-filters, and it couldrealize reversible integer transform by multi-lifting based on matrix factorization. Simulation results show that RTDLT-based compression system obtains comparable or even higher compression ratio in lossless compression than that of JPEG2000 and HD-Photo, better rate-distortion performance in lossy compression in most cases, and also gratify subjective visual quality.