Encyclopedia of Biophysics

Living Edition
| Editors: Gordon Roberts, Anthony Watts, European Biophysical Societies

Maximum Entropy Reconstruction

  • Jeffrey C. Hoch
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-35943-9_337-1

Maximum entropy (MaxEnt) reconstruction is a technique for computing frequency spectra from time series data, e.g., a free induction decay. It is based on the principle of information entropy introduced by Claude Shannon (1948). The MaxEnt spectrum contains the smallest amount of information consistent with the experimental data. In contrast to the discrete Fourier transform (DFT), MaxEnt references the measured data indirectly, enabling it to handle nonuniformly sampled (NUS, also called sparse sampling) data. Thus an important application of MaxEnt is the computation of multidimensional NMR spectra from NUS data.

Mathematically MaxEnt reconstruction is formulated as
$$ \operatorname{Maximize}\ \mathrm{S}\left(\mathbf{f}\right)\ \mathrm{subject}\ \mathrm{to}\ \mathrm{C}\left(\mathbf{d},\mathbf{m}\right)\le {\mathrm{C}}_0 $$
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Copyright information

© European Biophysical Societies' Association (EBSA) 2018

Authors and Affiliations

  1. 1.Molecular Biology and BiophysicsUConn HealthFarmingtonUSA

Section editors and affiliations

  • Mitsu Ikura

There are no affiliations available