Regularized spectral deconvolution ($F_{\lambda }=H^{\ast }G/(|H{|}^2+\lambda )$)

Tikhonov regularization of deconvolution can minimize $|HF-G{|}^2+\lambda |F{|}^2$ separately at each frequency. Completing the square gives $F_{\lambda }=H^{\ast }G/(|H{|}^2+\lambda )$ for $\lambda >0$. The regularization parameter trades reduced noise amplification against bias: the reconstruction multiplies the true noiseless component by $|H{|}^2/(|H{|}^2+\lambda )$ and the noise by $H^{\ast }/(|H{|}^2+\lambda )$.