Minimum range approach to blind partial simultaneous separation of bounded sources: Contrast and discriminacy properties

The blind source separation (BSS) problem is often solved by maximizing objective functions reflecting the statistical independence between outputs. Since global maximization may be difficult without exhaustive search, criteria for which all the local maxima correspond to an acceptable solution of the BSS problem are of interest. It is known that some BSS criteria used in a deflation procedure benefit from this property. More recently, the present authors have shown that the “spurious maximum free” property still holds for the minimum range approach to BSS in a simultaneous separation scheme. This paper extends the last result by showing that source demixing and local maximization of a range-based criterion are equivalent, even in a partial   separation scheme, i.e. when P⩽KP⩽K sources are simultaneously extracted from KK linearly independent mixtures of them.