Passive processing is interpretation of the noise and noise like signals received by an array of hydrophones. Our model assumes that there is an important noise component about which very little is known, that the data are stationary, that a long data sample is available, that signal wavefronts are planar, and that the response of the array to plane waves is known. We propose a processor and compare it with high‐resolution frequency‐wavenumber spectrum analysis. LetF̂denote an estimate of the spectral density matrix, and letHdenote any spectral density matrix that corresponds to a noise field composed of uncorrelated plane waves. A reasonable estimate of the spectral matrix of the signals and ambient noise is a value ofHfor whichF̂‐His positive semidefinite and traceHis maximized. The rationale for this estimate is closely related to a rationale for the estimate obtained by high‐resolution frequency‐wavenumber spectrum analysis (which is also called adaptive beamforming). The difference is that the former extracts the contribution from all directions at once, whereas the latter extracts the contribution from each direction separately. The former estimate rejects more unwanted noise than the latter.