The present invention describes a partial independent component (PICA) technique for blindly separating partially independent and/or gaussian-like sources from mixed observations over an informative index subspace, which allows various applications in independent component imaging. The present invention estimates a demixing matrix using only the independent and/or nongaussian portion of the observations. The present invention also demonstrates the principle of the approach on both controlled cases and real-world problems, and describes many extended applications of such a technique.