Optical detection and ranging in turbid waters are challenged by the effects of absorption and scattering. In particular, backscatter creates a clutter return, which can mask the presence of weak underwater targets. This work explores the use of independent component analysis (ICA), a statistical signal processing approach, to recover weak targets from strong backscatter in turbid waters using a frequency-modulated continuous-wave optical rangefinder. ICA uses statistical differences between target and backscatter returns to suppress the backscatter return. In laboratory test tank experiments, the use of ICA is observed to improve probability of detection at various turbidities and extend target detection range by four optical attenuation lengths.