Rapid development of sparse sampling methodology offers dramatic increase in power and efficiency of magnetic resonance techniques in medicine, chemistry, molecular structural biology, and other fields. We suggest to use available yet usually unexploited prior knowledge about the phase and the causality of the sparsely detected NMR signal as a general approach for a major improvement of the spectra quality. The work gives a theoretical framework of the method and demonstrates notable improvement of the protein spectra reconstructed with two commonly used state-of-the-art signal processing algorithms, compressed sensing and SIFT.