Implementations of the maximum entropy method for data reconstruction
have almost universally used the approach of maximizing the statistic
S - lambda chi(2), where S is the Shannon entropy of the reconstructed
distribution and chi(2) is the usual statistical measure associated w
ith agreement between certain properties of the reconstructed distribu
tion and the data. We develop here an alternative approach which maxim
izes the entropy subject to the set of constraints that chi(2) be at a
minimum with respect to the reconstructed distribution. This in turn
modifies the fitting statistic to be S - lambda .del chi(2) where lamb
da is now a vector. This new method provides a unique solution to both
the well-posed and ill-posed problem, provides a natural convergence
criterion which has previously been lacking in other implementations o
f maximum entropy, and provides the most conservative (least informati
ve) data reconstruction result consistent with both maximum entropy an
d maximum likelihood methods, thereby mitigating against overinterpret
ation of reconstruction results. A spectroscopic example is shown as a
demonstration.