Currently NMR spectra are generated by Fourier transformation of free induction decay curves from time domain to frequency domain. In the late 60 s-80s some researchers proposed reconstruction of NMR spectra using a mathematical technique called "entropy maximization" from the FIDs. Fourier transformation was involved but only during intermediate steps. Just a note that this entropy maximization has nothing to with classical thermodynamics. It is a constraint optimization technique for reconstructing images with least amount of information. Consider entropy as just a mathematical function which shares the same name (thanks to Shannon) as the thermodynamic entropy.
Papers from the 1980s (e.g. Nature volume 311, pages446–447 (1984)) show that the appearance wise signal-to-noise ratio is higher in the MaxEnt reconstructed NMR spectrum as compared to standard FT method. However, in the Journal of Magnetic Resonance, this idea has been contested, as one cannot get something out of nothing. Some authors say, especially Hoch et al., that this is just a cosmetic exercise, because MaxEnt reduces the noise in the baseline but not in the peak. Therefore, the signal-to-noise ratio improves, but the sensitivity is no better. However, others say that MaxEnt is still very useful, and they contested that Hoch’s calculations were not realistic.
Very crudely, graphically the standard approach is:
but MaxEnt reconstructed NMR does the following magic as shown below. Since we have a couple of expert NMR spectroscopists here, my question is why MaxEnt technique never caught up in mainstream NMR? If it were so good at enhancing SNR, conventional FT should have become obsolete. I understand that it is a very involved calculation, but it looks too promising to an outsider.