Implementing the Minimum-Extent Criterion for Solving Linear Inverse Problems

We present a numerical implementation of a novel approach for solving linear inverse problems, based on the dual requirement of minimizing both the quasi-extent of the solution residual and the quasi-extent of the solution itself. The implementation employs the conjugate gradient method, where each descent step targets the minimization of either the residual’s quasi-extent (the first component of the objective function), the solution’s quasi-extent (the second component of the objective function), or the full objective function under a quadratic approximation near its minimum. This approach implementation is applicable for constructing digital twins of dipole radiation sources in environments affected by noise and outliers.