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The authors propose a new solution to the blind separation of sources (BSS) based on statistical independence. In the two-dimensional (2-D) case, we prove that, under the whiteness constraint, the fourth-order moment-based approximation of the marginal entropy (ME) cost function yields a sinusoidal objective function. Therefore, we can minimize it by simply estimating its phase. We prove that this estimator is consistent for any source distribution. In addition, such results are useful for interpreting other algorithms such as the cumulant-based independent component analysis (CuBICA) and the weighted approximate maximum likelihood (WAML) [or weighted estimator (WE)]. Based on the WAML, we provide a general unifying form for several previous approximations to the ME contrast. The bias and the variance of this estimator have been included. Finally, simulations illustrate the good consistency, convergence, and accuracy of the proposed method.