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Conjugate gradient algorithm

The pattern-based method can be described as the constrained linear equation system:

\begin{equation*}\begin{aligned}\mathbf{0} & \approx \mathbf{NNs} - \mathbf{NNd} \mathbf{0} & \approx \epsilon \mathbf{Ds} \end{aligned}\end{equation*}

where $ \mathbf{NN}$ denotes the chain operator, which applies operator $ \mathbf{N}$ twice. The following conjugate gradient algorithm (Wang, 2016) can be used to solve such problem.
\begin{algorithm}{Conjugate gradients with regularization}
{\mathbf{NN}, \mathb...
...ight] \\
\hat{\rho} \= \rho
\end{FOR} \\
\RETURN \mathbf{s}