A system and method allow for extracting target signals from the overall measurement data without knowing how and where these data are collected, the locations and characteristics of target sources as well as those of random background noise sources. In essence, it uses an innovative and advanced signal processing technique to reveal certain critical information from a mixture of data that is hard to obtain otherwise. In particular, it allows for denoising the measured data that have been contaminated by various interfering and background noise, making it possible to extract certain target information that may be otherwise difficult to observe. The only assumption made in this method is that the target signal is incoherent with respect to all interfering signals and background noise. The more information about a target signal is available, the more complete the extracted signal becomes.