# Could kernel density map be recovered with known kernel function?

I'm confused whether a KDE map could be recovered with known kernel function. The KDE map (with no noise) generated with fast fourier trasnformation (FFT) could be recovered on very high accuracy (<10e-3) in my experiment. The equations are as follows:

G(u,v)=H(u,v)*F(u,v)

F(u,v)=G(u,v)/H(u,v)

G(u,v) is the fourier transformation of density map

F(u,v) is the fourier transformation of original map

H(u,v) is the fourier transformation of kernel density function

But the KDE map generated by regular convolution method is very different to be recovered. I'm confused about those opposite answers. Anybody could tell "whether or not a kernel density map could be recovered?"

Many thanks!