Figure 4

Fourier shell correlation (FSC) of the vector tomography reconstruction of the simulated data using regularziers: (a) \(l_2\) norm \(\Vert {\textbf {M}}\Vert\), (b) squared \(l_2\) norm \(\Vert {\textbf {M}}\Vert ^2\) and (c) squared \(l_2\) norm of the gradient \(\Vert \nabla M_x\Vert ^2 + \Vert \nabla M_y\Vert ^2 + \Vert \nabla M_z\Vert ^2\). The high-frequency information improves under the squared \(l_2\) norm regularizer while the low-frequency information decreases. In contrast, the squared \(l_2\) norm of the gradient enhance the low-frequency information via smoothing but destroy some important high-frequency information. The \(l_2\) norm regularizer worsens the signal since it is not a proper regularizer for this case.