# Tikhonov regularization

The Tikhonov regularization is a simple method to deal with ill-conditionned inverse problems. The measured data $$y$$ is modeled by $y = Hx + n$ where $$n$$ is a measurement noise, usually assumed white and gaussian. The estimate $$\hat x_\lambda$$ is found by solving the optimization problem $\hat x_\lambda = \mathrm{argmin}_x \|y - Hx\|_2^2 + \lambda \|\Gamma x\|_{2}^2$ where $$\Gamma$$ is matrix modeling priori information about $$x$$, and $$\lambda$$ is the regularization parameter.

Here, $$\Gamma$$ is chosen to be the identity operator, first derivative, or second derivative

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