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The generalized inverse method and singular value decomposition were used to reconstruct the magnetic image of small spherical inclusions in ferromagnetic structures. These techniques were used on the magnetic flux leakage generated when the structure is magnetized. The leakage field from the inclusions was simulated by using a simple constantpermeability model. The recovery model used a grid of magnetic dipoles at the region of the inclusions. The ability of the. technique to distinguish between different distributions of inclusions with similar leakage fields is analyzed. The results demonstrates the feasibility of imaging multiple inclusions within the structure.

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Intrinsic dimension and differential entropy estimators are studied in this paper, including their systematic bias. A pragmatic approach for joint estimation and bias correction of these two fundamental measures is proposed. Shared steps on both estimators are highlighted, along with their useful consequences to data analysis. It is shown that both estimators can be complementary parts of a single approach, and that the simultaneous estimation of differential entropy and intrinsic dimension give meaning to each other, where estimates at different observation scales convey different perspectives of underlying manifolds. Experiments with synthetic and real datasets are presented to illustrate how to extract meaning from visual inspections, and how to compensate for biases.