A fast algorithm for determining phase values for symbols from weighted symbol relations in direct methods

The use of symbols to express phases in direct methods leads to relations between symbols (symbol relations). The relative probability of a symbol relation is defined in such a way that it has additive properties. The algorithm given in this paper is developed for the deconvolution of the symbols and is applicable to symmetric phases (0 or π) and to anti-symmetric phases (+½ π or --½ π); weighted symbol relations are used as input and figures of merit are calculated for all permutations of phases for the symbols. The algorithm is especially useful when a large number of symbols is used.