Local normalization

Both (H)CTRI and ATRI suffer from a common drawback: the multiplication of wavefields destroys phase information and leads to an exponential growth of relative amplitudes. To deal with the issue of unbalanced amplitudes, we design a local normalization operator with a sliding-window

$$M(\mathbf{x},t) = \frac{I(\mathbf{x},t)}{\max\left[I(\mathbf{x},t-\tau/2:t+\tau/2)\right]} \;,$$ (4)

where $\tau$ is the window size. This operator normalizes a time-slice of the wavefield by the maximum value in a local window centered around the time $t$. More sophisticated windows can be designed by the same principle, for example, by making the local window variable in space.