Combined Data and Model Residuals

To compute the optimal set of $\bold m_i$, a quadratic objective function, $Q(\bf m)$, consisting of sum of the weighted norms of a data residual [equation (7)] and of two model residuals [equations (8) and (9)], is minimized via a conjugate gradient scheme:  

$$\mbox{min} Q(\bold m) \; = \; \Vert \bold r_d \Vert^2 \; + \... ...1]} \Vert^2 \; + \; \epsilon_x^2 \Vert \bold r_m^{[2]} \Vert^2$$ (10)

$\epsilon_m$ and $\epsilon_x$ are scalars which balance the relative weight of the two model residuals with the data residual.