Regularized spectral deconvolution (source code)

= Regularized spectral deconvolution
{title2=$F_\lambda=H^*G/(|H|^2+\lambda)$}

<Tikhonov regularization> of <deconvolution> can minimize $|HF-G|^2+\lambda|F|^2$ separately at each <frequency>. Completing the square gives $F_\lambda=H^*G/(|H|^2+\lambda)$ 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 $H^*/(|H|^2+\lambda)$.