Walter Rudin's scientific contributions

... However, the flexibility Σ ∈ S ++ N (i.e., considering correlation rather than coherence coefficients) is required in order to conduct proper mathematical derivations, and to ensure the algorithmic stability of the maximum likelihood estimator algorithms: there is, to the best of our knowledge, no explicit (nor tractable) maximum likelohood estimator for the modulus-argument decomposition when assuming some additional phase and/or low-rank structure in the covariance matrix. This is because the modulus and argument are not holomorphic functions [17,18]. This also probably explains why most related works rely on plug-in estimates of the matrix Υ, as observed in [9] (which also implicitly reformulates phase-linking using the real core parameterization). ...