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It introduces an algebraic approach based on tensor factorization. For k spikes, suggests taking about k log k random locations in Fourier space, plus d deterministic locations, and then sampling on a grid of size (k log k d) 3 corresponding to all ways of summing three of these locations. Because of the algebraic properties of Fourier measurements, the resulting 3-tensor is of rank k (up to noise). The paper proves that with high probability in the sample locations, the matrix of factors is well-conditioned, and hence the factors can be stably recovered using linear algebraic manipulations. These results are stable under small deterministic noise.