1.9.2.4 Formalism of maximum entropy method (MEM) Maximum entropy method can be used to determine the electron density in the unit cell from the phased X-ray diffraction data. MEM method attempts to extract the maximum amount of information from the data, without introducing assumptions (or) artifacts as they may be the result of employing a model [Smaalen et al., 2009]. At the very first, MEM image technique was employed in radio astronomy. Later it has found applications in image processing, the analysis of any type of spectroscopic (or) diffraction data. MEM is now vastly used in crystallographic applications and to determine most probable electron density distributions in the unit cell of a particular system under investigation, and locating…show more content… The theory of maximum entropy method (MEM) is understandable with some equations which are similar to the equations in statistical thermodynamics because the information entropy and statistical entropy deal with the concept of most probable distribution. In the statistical thermodynamics the distribution of the particles in phase space are considered where as in the information theory the distribution of numerical quantities over the ensemble of pixels is considered. The probability distribution of N identical particles over m boxes each contains ni particles can be written…show more content… Since the numerator in equation 1 is constant, the entropy is written as ………….1.26
Where, Stirlings’ formula lnN!≈N lnN-N has been used.
When there is a prior probability qi for the ith box to contain ni number of particles. This can be expressed by, ………….1.27
Which then gives the expression for entropy,