Noises by incipient propeller tip vortex cavitation (TVC) are generally generated at regions near the propeller tip. Localization of these sparse noises is performed using compressive sensing (CS) with measurement data from cavitation tunnel experiments. Since initial TVC sound radiates in all directions as a monopole source, a sensing matrix for CS is formulated by adopting spherical beamforming. CS localization is examined with known source acoustic measurements, where the CS estimated source position coincides with the known source position. Afterwards, CS is applied to initial cavitation noise cases. The result of cavitation localization was detected near the upper downstream area of the propeller and showed less ambiguity compared to Bartlett spherical beamforming. Standard constraint in CS was modified by exploiting the physical features of cavitation to suppress remaining ambiguity. CS localization of TVC using the modified constraint is shown according to cavitation numbers and compared to high-speed camera images.