Correction: Dynamical machine learning volumetric reconstruction of objects’ interiors from limited angular views

Correction to: Light: Science & Applications

https://doi.org/10.1038/s41377-021-00512-x, published online 07 April 2021

Iksung Kang, Alexandre Goy, George Barbastathis

We are correcting Eq. (8) on p. 16 and Eq. (10) on p. 17, which were inadvertently missing sigmoid functions ($\sigma$).

Eq. (8) should be corrected as:

$$r_m = \sigma \left( {W_r\xi _m + U_rh_{m - 1} + b_r} \right)$$

$$z_m = \sigma \left( {W_z\xi _m + U_zh_{m - 1} + b_z} \right)$$

$$\tilde h_{{{\mathrm{m}}}} = \tanh \left( {W\xi _m + U\left( {r_m \circ h_{m - 1}} \right) + b_h} \right)$$

$$h_m = \left( {1 - z_m} \right) \circ \tilde h_m + z_m \circ h_{m - 1}$$

and Eq. (10) should be corrected as:

$$r_m = \sigma \left( {W_r \ast \xi _m + U_r \ast h_{m - 1} + b_r} \right)$$

$$z_m = \sigma \left( {W_z \ast \xi _m + U_z \ast h_{m - 1} + b_z} \right)$$

$$\tilde h_{{{\mathrm{m}}}} = {{{\mathrm{ReLU}}}}\left( {W \ast \xi _m + U \ast \left( {r_m \circ h_{m - 1}} \right) + b_h} \right)$$

$$h_m = \left( {1 - z_m} \right) \circ \tilde h_m + z_m \circ h_{m - 1}$$

The code is publicly available at https://github.com/iksungk.

The original article has been updated.