Information: to Harvest, to Have and to Hold

Signal-to-Noise Ratios (SNRs) and the Shannon-Hartley channel capacity are metrics that help define the loss of known information while transferring data through a noisy channel. These metrics cannot be used for quantifying the opposite process: the harvesting of new information. Correlation functions and correlation coefficients do play an important role in collecting new information from noisy sources. However, Bershad and Rockmore [1974] based their formulas on contradictory a priori assumptions in Real-space and in Fourier-space. Their formulations were subsequently copied literally to the practical science of electron microscopy, where those a priori assumptions now distort most quality metrics in Cryo-EM. Cryo-EM became a great success in recent years [Wiley Award 2017; Nobel prize for Chemistry 2017] and became the method of choice for revealing structures of biological complexes like ribosomes, viruses, or corona-virus spikes, vitally important during the current COVID-19 pandemic. Those early misconceptions now interfere with the objective comparison of independently obtained results. We found that the roots of these problems significantly pre-date those 1970s publications and were already inherent in the original SNR definitions. We here propose novel metrics to assess the amount of information harvested in an experiment, information which is measured in bits. These new metrics assess the total amount of information collected on an object, as well as the information density distribution within that object. The new metrics can be applied everywhere where data is collected, processed, compressed, or compared. As an example, we compare the structures of two recently published SARS-CoV-2 spike proteins. We also introduce new metrics for transducer-quality assessment in many sciences including: cryo-EM, biomedical imaging, microscopy, signal processing, photography, tomography, etc.
Comment: 43 pages, 10 Figures