Fast adaptive optimization of weighted vector median filters

Weighted vector median (WVM) filters are effective tools for multichannel signal processing. To obtain the desired filtering behavior and characteristic, the WVM filter weights must be determined in an appropriate manner. In this paper, we first analyze previously defined approaches for WVM filter optimization and show their drawbacks related to derivative computation and vector direction information utilization. Based on this analysis, we propose two fast adaptive algorithms for WVM filter design. Proposed Algorithm I computes locally optimal weight changes at each iteration and updates the filter weights accordingly. This algorithm does not involve derivative computation, thus eliminating the instability caused by derivative approximations utilized in previous approaches. Proposed Algorithm II extends the results from established marginal weighted median optimization methods to the vector case by error metric generalization. Both algorithms can be applied to WVM filters using the L_p norm, while Algorithm I can operate on more general distance metrics. The presented simulation results show that both algorithms are effective, fast, and stable; they perform well under a wide range of circumstances