We discuss the measurement of noise-initiated Brillouin scattered power in optical fibers and its application to distributed sensing systems. In particular, we consider the use of Brillouin scattering in the nonlinear regime, demonstrating a novel processing technique that compensates for the nonlinear growth of the scattered signals. The signal-to-noise ratio performance of this technique is evaluated, highlighting the importance of the noise contributed by the random statistics of the scattered field and yielding the conditions for optimum system operation.