Gaussian deconvolution via differentiation

Suppose that ϕ is a Gaussian density and that g = f * ϕ, where * denotes convolution. From observations with density g, one wishes to estimate f. We analyze an estimate which is a linear combination of estimates of derivatives of g and show that this estimate converges in an L2 norm at a rate which is compatible with the pointwise optimal rate established by Fan (1991).