  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.
