Accelerating the data acquisition is one of the major developments in modern Nuclear Magnetic Resonance (NMR). Non-Uniform Sampling (NUS) acquires fewer data and reconstructs the spectra with proper signal processing methods1. Here, we introduce an approach to reconstruct faithful spectra from highly accelerated NMR. The FID signal is constrained by the self-learning signal subspace (SLS), in which a true representation of NMR should be in. Results on realistic NMR data demonstrate that the new approach provides much better spectra than the compared state-of-the-art method.