PROGRAMS FOR SIGNAL RECOVERY FROM NOISY DATA USING THE MAXIMUM-LIKELIHOOD PRINCIPLE .1. GENERAL DESCRIPTION

A program package for nonnegative signal recovery from noisy experimental data distorted by the measuring device is presented. Noise may have a Gaussian, binomial or Poissonian distribution at each experimental point. Three examples are given which demonstrate the usage of the package: (a) reduction to an arbitrary instrumental function, which depends only on the difference of its argument (this is the typical spectroscopic problem); (b) the expansion of an exponentially decaying curve which has a continuous spectrum of decrements (this problem has applications in time dependent fluorescence, nuclear physics etc.); and (c) the ultrasoft X-ray spectrum recovery from absorption measurements. These programs are based on the maximum likelihood principle which allows the maximum value of resolution enhancement according to Shannon's information theory to be achieved.