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5

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 $\boldsymbol{x} \sim N \left( 0, {\sigma}_{x}^{2} \right)$....

4

I'd say there 3 approaches to do so: Properties of the LMS Filter There is an optimal step size given you know the spectrum of the correlation matrix. You may have a look at Wikipedia's Least Mean Squares Filter at Convergence and Stability in the Mean. Some other approaches related to this might be those from Variable Step Size LMS. You may have a look at ...

0

The result is significantly better if I weight the operator so that each "column" has unit norm: I change the operator to $P^HF^HWm$, where $W$ is a weight so that the output of the operator has unit norm when applied to an $m$ that is zero except for any one element, which is set to one (either the real or imaginary component).

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