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Usually Tikhonov Regularization is applied in the following form:
$$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| A \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \frac{\lambda}{2} {\left\| \boldsymbol{x} \right\|}_{2}^{2} $$
This formulation can be seen as:
MAP Estimator with the prior of $ \boldsymbol{x} \sim N \left( 0, {\sigma}_{x}^{2} \right) $....
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