  Solar activity is usually caused by the evolution of solar magnetic fields.
Magnetic field parameters derived from photospheric vector magnetograms of
solar active regions have been used to analyze and forecast eruptive events
such as solar flares and coronal mass ejections. Unfortunately, the most recent
solar cycle 24 was relatively weak with few large flares, though it is the only
solar cycle in which consistent time-sequence vector magnetograms have been
available through the Helioseismic and Magnetic Imager (HMI) on board the Solar
Dynamics Observatory (SDO) since its launch in 2010. In this paper, we look
into another major instrument, namely the Michelson Doppler Imager (MDI) on
board the Solar and Heliospheric Observatory (SOHO) from 1996 to 2010. The data
archive of SOHO/MDI covers more active solar cycle 23 with many large flares.
However, SOHO/MDI data only has line-of-sight (LOS) magnetograms. We propose a
new deep learning method, named MagNet, to learn from combined LOS
magnetograms, Bx and By taken by SDO/HMI along with H-alpha observations
collected by the Big Bear Solar Observatory (BBSO), and to generate vector
components Bx' and By', which would form vector magnetograms with observed LOS
data. In this way, we can expand the availability of vector magnetograms to the
period from 1996 to present. Experimental results demonstrate the good
performance of the proposed method. To our knowledge, this is the first time
that deep learning has been used to generate photospheric vector magnetograms
of solar active regions for SOHO/MDI using SDO/HMI and H-alpha data.
