[2] L₂ norm or cost function definition

Based on least-squares theory, a minimizing problem can be defined, which aims to find $\delta m^{*}$ in order to minimize the cost function. The L₂ norm or cost function definition is given by  

$$f\left(\delta \textbf{m} \right) =\Vert A \delta \textbf{m}-\delta \textbf{d} \Vert^{2}_{2} .$$ (29)

In order to constrain the inverse problem, or to use some prior information to bound the solution of the inverse problem, regularization is commonly used. In this case, the cost function needs to be modified.