Frequency-Domain Implementation of Regularization

Regularization methods play an important role in solving linear equations of the form $$ y=Hx, $$ with prior knowledge about the solution. The corresponding regularization results in minimization of $$ f(x)={\left\Vert y-Hx\kern0.1em \right\Vert}^2+\lambda {\left\Vert \kern0.1em Cx\kern0.1em \right\Vert}^2. $$