As p is reduced the solutions will become increasingly sparse. When p = 1 [17] the problem can be modified slightly to be recast as a linear program which can be solved by a simplex method. In this case it is the sum of the absolute values of the solution components that is minimized. Although the solutions obtained with this norm are sparser than those obtained with the L2 norm, the orientation results were found to be less clear [17]. Another difference is that while the localization results improve if the number of electrodes is increased in the case of the L2 approach, this is not the case with the L1 approach which requires an increase in the number of grid points for correct localization. A third difference is that while both approaches perform badly in the presence of noisy data, the L1 approach performs even worse than the L2 approach. For p < 1 it is possible to show that there exists a value 0 <p < 1 for which the solution is maximally sparse. The non-quadratic formulation of
