We propose a new class of mapping-based nonlinear quadratic Volterra filters for image enhancement. The input signal is mapped prior to filtering by a emoryless one-to-one nonlinear mapping function. The mapping function can be described by any arbitrary function and implemented by a simple look-up table. necessary, an inverse mapping function is applied after filtering. Using this general approach, the quadratic Volterra filter output can be adjusted to a desired response. Some results are presented where a highpass quadratic Volterra filter is used to enhance an image by unsharp masking.