Methods are presented for deriving the density field and the resulting linear-theory velocity field from an all-sky redshift survey of IRAS galaxies. The luminosity function of IRAS galaxies is measured using a maximum-likelihood technique independent of density inhomogeneities. Within its range of validity, it is found to be in excellent agreement with previously published luminosity functions. Self-consistent solutions for the true spatial positions of the IRAS galaxies are found, given their redshifts and peculiar velocities. The ambiguity inherent in triple-valued regions is overcome either by sufficient smoothing, or by using prior information from peculiar velocity maps obtained independently.
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Yahil et al. (1991) studied this question.