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In this paper, we show that sparse signals f representable as a linearcombination of a finite number N of spikes at arbitrary real locations or as afinite linear combination of B-splines of order m with arbitrary real knots canbe almost surely recovered from O(N^2) Fourier intensity measurements up totrivial ambiguities. The constructive proof consists of two steps, where in thefirst step the Prony method is applied to recover all parameters of theautocorrelation function and in the second step the parameters of f arederived. Moreover, we present an algorithm to evaluate f from its Fourierintensities and illustrate it at different numerical examples.

Sparse phase retrieval of one-dimensional signals by Prony's method