Parametric projection filter for image and signal restoration

A class of linear algebraic restoration filters is derived for the linear degradation model with additive noise. The filters are based on an optimization criterion involving two effects: first, the error in the restored noiseless image compared to the original image, and second, the energy of additive noise passed through the restoration. These two effects can be balanced with a scalar parameter. For both error types, explicit expressions are derived in terms of the parameter. It is shown that by allowing the first error norm to grow slightly, the noise energy may be considerably reduced. This also has a bearing on the analysis of the behavior of other linear parametric restoration filters.