Algorithm 1

procedure

Set a value for λ

Pick initial values for $\widehat{\mathbf{c}},{\widehat{\mathit{\theta }}}^{\prime }$

Inner optimization loop:

Estimate $\widehat{\mathbf{c}}$ by minimizing $J_{in}\left({\widehat{\mathbf{c}}}^{\prime }|{\mathit{\theta }}^{\prime },\mathit{\lambda }\right)$

given by Eq. (4)

Outer optimization loop:

Estimate ${\widehat{\mathit{\theta }}}^{\prime }$ by minimizing $J_{out}\left({\mathit{\theta }}^{\prime }|\mathbf{y},\mathbf{\lambda }\right)$

given by Eq. (5)

if ${\widehat{\mathit{\theta }}}^{\prime }$ are changed (to within some preset precision), $J_{in}\left({\widehat{\mathbf{c}}}^{\prime }|{\mathit{\theta }}^{\prime },\mathbf{\lambda }\right)$ is reoptimized with respect to $\widehat{\mathbf{c}}$ then goto Inner optimization.

else ${\widehat{\mathit{\theta }}}^{\prime }={\mathit{\theta }}^{\prime }.$

close;