Quadratic-linear filters for signal detection

The second-order Volterra series (quadratic-linear) filter was synthesized under three different optimization criteria for signal detection. The performance of the filters is shown to exceed that of quadratic-only or linear-only filters when the noise process is characterized by both separation in the mean and separation in variance. The applications are in object detection and image segmentation, especially in model-drive approaches to these problems. For 2-D applications, the mapping order of pixels into the signal vector is shown to have no effect on the optimality of the filters, regardless of nonlinearity