Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory

A fast non-convex low-rank matrix decomposition method for potential field data separation is presented. The singular value of the large size trajectory matrix, which also a block Hankel obtained using randomized algorithm in matrix-vector multiplications are implemented with minimal memory storage. This integrated into \begin{document}$\text{Altproj}$\end{document} algorithm, standard solving robust principal component analysis optimization problem. integration this improved estimation partial avoids construction Hence, gravity and magnetic matrices can be computed achieved better computational efficiency. presented and, hence, algorithm-dependent parameters easily determined. performance without efficient low rank contrasted synthetic different sizes. These results demonstrate that not only computationally more but it accurate. Moreover, possible to solve far larger problems. As an example, adopted environment, sizes than id="M2">\begin{document}$ 205 \times $\end{document} generate "out memory" exceptions improvement, whereas id="M3">\begin{document}$ 2001\times 2001 now calculated id="M4">\begin{document}$ 1062.29 $\end{document}s. Finally, applied separate real Tongling area, Anhui province, China. Areas may exhibit mineralizations inferred based on separated anomalies.