  Direct imaging of impressed dc currents inside the head can provide valuable
conductivity information, possibly improving electro-magnetic neuroimaging.
Ultra-low field magnetic resonance imaging (ULF MRI) at $\mu$T Larmor fields
can be utilized for current density imaging (CDI). Here, a measurable impact of
the magnetic field $B_{J}$, generated by the impressed current density $J$, on
the MR signal is probed using specialized sequences. In contrast to high-field
MRI, the full tensor of $B_{J}$ can be derived without rotation of the subject
in the scanner, due to a larger flexibility in the sequence design. We present
an ULF MRI setup based on a superconducting quantum nterference device (SQUID),
which is operating at a noise level of 380 aT Hz$^{-1/2}$ and capable of
switching all imaging fields within a pulse sequence. Thereby, the system
enables zero-field encoding, where the full tensor of $B_{J}$ is probed in the
absence of other magnetic fields. 3D CDI is demonstrated on phantoms with
different geometries carrying currents of approximately 2 mA corresponding to
current densities between 0.45 and 8 A/m$^{2}$. By comparison to an in vivo
acquired head image, we provide insights to necessary improvements in
signal-to-noise ratio.
