The maximum determinant method and the maximum entropy method

A generalized maximum determinant rule is shown to be equivalent to maximizing the integral, of the logarithm of the electron density, i.e. equivalent to the 'maximum entropy method' (MEM) of image reconstruction. Relations between the structure factors and the Fourier coefficients of the reciprocal of the electron density follow, leading to new algorithms for phase determination and refinement. Although structures with equal, spherical, resolved atoms automatically satisfy the MEM phase relations, the method really requires only positivity and 'peakiness' of the electron density.