Update nonlinear Signal

Projection

\(S_{mk}' = \sum_{n}D_{kn} \cdot \mathrm{sgn}(T_{mn}^{\mathrm{exp}})\cdot\sqrt{|T_{mn}^{\mathrm{exp}}|} \dfrac{S_{mn}}{|S_{mn}|}\)

Iteration

\(S_{mk}' = S_{mk} - \alpha\eta\cdot\nabla_{mk}r\)

Intensity

\(r = \sum_n(T_{mn}^{\mathrm{exp}} - \mu T_{mn})^2\)

\(\nabla_{mk}r = \frac{dr}{dS_{mk}^*} = -2\sum_n D_{kn}(\frac{T_{mn}^{\mathrm{exp}}}{\mu} - T_{mn})\cdot S_{mn}\)

\(H_{zz} = \sum_n D_{kn}D_{nj} (2T_{mn} - \frac{T_{mn}^{\mathrm{exp}}}{\mu})\)

Magnitude

\(r=\sum_n(\sqrt{T_{mn}^{\mathrm{exp}}} - \mu |S_{mn}|)^2\)

\(\nabla_{mk}r = \frac{dr}{dS_{mk}^*} = -2\sum_n D_{kn}(\sqrt{T_{mn}^{\mathrm{exp}}}\cdot\frac{S_{mn}}{\mu|S_{mn}|} - S_{mn})\)

\(H_{zz} = \sum_n D_{kn}D_{nj}\)