  Radio frequency (RF) spike noise is a common source of exogenous image
corruption in MRI. Spikes occur as point-like disturbances of $k$-space that
lead to global sinusoidal intensity errors in the image domain. Depending on
the amplitude of the disturbances and their locations in $k$-space, the effect
of a spike can be significant, often ruining the reconstructed images. Here we
present both a spike detection method and a related data correction method for
automatic correction of RF spike noise. To detect spikes, we found the
$k$-space points that have the most significant effect on the total variation
of the image. To replace the spikes, we used a compressed sensing
reconstruction in which only the points thought to be corrupted are
unconstrained. We demonstrated our technique in two cases: (1) in vivo gradient
echo brain data with artificially corrupted points and (2) actual, complex
scanner data from a whole-body fat-water imaging gradient echo protocol
corrupted by spikes at uncertain locations. Our method allowed near-perfect
detection and correction with no human intervention. We calculated Matthews
correlation coefficients and sensitivities above 0.95 for a maximum of 0.78\%
corruption in synthetically corrupted in vivo brain data. We also found
specificities above 0.9994.
