  Time-resolved magnetic sensing is of great importance from fundamental
studies to applications in physical and biological sciences. Recently the
nitrogen-vacancy (NV) defect center in diamond has been developed as a
promising sensor of magnetic field under ambient conditions. However the
methods to reconstruct time-resolved magnetic field with high sensitivity are
not yet fully developed. Here, we propose and demonstrate a novel sensing
method based on spin echo, and Haar wavelet transform. Our method is
exponentially faster in reconstructing time-resolved magnetic field with
comparable sensitivity over existing methods. Further, the wavelet's unique
features enable our method to extract information from the whole signal with
only part of the measuring sequences. We then explore this feature for a fast
detection of simulated nerve impulses. These results will be useful to
time-resolved magnetic sensing with quantum probes at nano-scales.
