With the development of promising cavitation-based treatments, the interest in cavitation monitoring with passive acoustic mapping (PAM) is significantly increasing. While most of studies regarding PAM are performed in 2-D, 3-D imaging modalities are getting more attention relying on either custom-made or commercial matrix probes. Unless specific phased-arrays are used for a specific application, limitations due to probe apertures often results in poor performances of the 3-D mapping, due to the use of a delay-and-sum (DAS) classic beamformer, which results in strong artifacts and large main lobe sizes. In this article, 3D-PAM is achieved by performing adaptive beamforming in the frequency domain (FD) in 3-D, and using a random sparse apodization of a commercial matrix array driving only 256 elements among the 1024 available. It reduces the computation time and makes use of only one 256-channel research platform. Three beamformers have been implemented in 3-D and in the FD: the DAS beamformer, which corresponds to the beamformer used in previous 3D-PAM studies, the robust capon beamformer (RCB), an adaptive algorithm widely used in 2D-PAM for its high performances, and the MidWay (MW) beamformer, an adaptive algorithm with a computation complexity equivalent to the one of DAS. These algorithms are evaluated both in simulations and experiments with a harmonic source at different positions, and are also applied to real cavitation signals. The results show that, in the case of matrix arrays of small aperture such as generic commercial matrix probes, the DAS beamformer leads to large main lobe sizes, while adaptive beamformers largely improve the performances of the mapping. The low computation time and its parameter-free character make MW beamformer a good compromise for 3D-PAM applications. It thus appears that a random sparse apodization combined with adaptive beamforming is a good solution to achieve high-performance 3D-PAM with manageable devices.