In noisy conditions, this constraint can be incorporated as a minimum norm side constraint, giving rise to the minimum norm estimate (MNE) [81]. Other variations of the MNE include the lead-field normalized weighted minimum norm (WMN) [82], low-resolution brain electromagnetic tomography (LORETA) [83], and their extensions to statistical mapping [21, 84], etc. The common feature shared by these algorithms is the linearity of the inverse solution, meaning that the inverse solution can be obtained through transforming the measurements through a linear system (or inverse matrix). The linear inverse solutions return low-resolution images of current density or its statistics. Iterative algorithms have been developed to enhance the focal sources [85]. These iterative methods have been suggested to be equivalent to a nonlinear inverse solver that minimizes a cost function formulated with L-p norms for both the data fitting term and the side constraint [86]. This is in line with other nonlinear inverse algorithms that specifically utilize the solution constraint other than the L-2 norm, such as the minimum current estimation (MCE) [87], L1 norm [88–90] and L-p norm [91].
