  We present a comprehensive study based on multi-wavelength observations from
the NuSTAR, NICER, Swift, Fermi, NEOWISE, and ATCA telescopes during the 2022
outburst of the black hole X-ray binary IGR J17091-3624. Our investigation
concentrates on the heartbeat-like variability in the X-ray emission, with the
aim of using it as a tool to unravel the origin of the non-thermal emission
during the heartbeat state. Through X-ray timing and spectral analysis, we
observe that the heartbeat-like variability correlates with changes in the disk
temperature, supporting the disk radiation pressure instability scenario.
Moreover, in addition to a Comptonization component, our time-averaged and
phase-resolved spectroscopy reveal the presence of a power-law component that
varies independently from the disk component. Combined with the radio to X-ray
spectral energy distribution fitting, our results suggest that the power-law
component could originate from synchrotron self-Compton radiation in the jet,
which requires a strong magnetic field of about $B = (0.3$-$3.5)\times10^6$ G.
Additionally, assuming that IGR J17091-3624 and GRS 1915+105 share the same
radio-X-ray correlation coefficient during both the hard and the heartbeat
states, we obtain a distance of $13.7\pm2.3$ kpc for IGR J17091-3624.
