Time-reversal imaging is a powerful technique for localizing passive seismic sources. It is robust independent of the source time and applicable to heterogeneous media. However, time-reversal imaging usually requires a dense, uniform, and large-aperture acquisition that provides sufficient illumination to accurately localize passive seismic sources. This requirement often is not met in practice. In many field data cases, apertures are an insufficient and spatial sampling of the recorded wavefield is irregular and sparse because of complex topographical conditions, technical issues, budget problems, etc. For a sparse and small-aperture acquisition, it is difficult to identify events using common time-reverse imaging procedures because of strong imaging artifacts leading to false positives. To mitigate these problems, we have proposed a new approach that evaluates maximum-amplitude paths constructed from back-projected wavefields using receiver patches selected from the acquisition. These paths are built by scanning for the maximum absolute amplitude of the back-propagated wavefronts within a spatial dimension of the dominant wavelength of the considered event. The paths comprise maximum amplitudes of the back-projected wavefronts for each considered time step. The methods exploit the continuity of maximum amplitudes of the back-projected wavefields. The point of closest proximity (or crossing point) of the paths denotes the source location and the corresponding time is the source time. Numerical examples for the Marmousi-II and SEG 3D overthrust models indicate that the proposed approach can estimate the source excitation time and source localization simultaneously for sparse and small-aperture acquisitions of noisy data with high accuracy. Source excitation time errors are below the prevailing period, and maximum localization errors are below the dominant wavelength, that is, within the resolution of band-limited signals. Using a wide aperture acquisition, these results are further improved and lead to errors in the order of the spatial and temporal sampling.