Recent research suggests that it's possible to reconstruct the seismic data using non-convex -norm minimization, . Particularly, iterative half thresholding has been developed both in signal processing and exploration geophysics communities (Yang et al., 2013a; Xu et al., 2012). The difference between half thresholding and the conventional soft thresholding is just the thresholding operator. When ,
becomes a half-thresholding operator:
can be constant, linear-decreasing (Abma and Kabir, 2006) and exponential-decreasing (Gao et al., 2010). However, all of these defining criterion are based on a prior knowledge about the data and is often not easy to choose. Instead, a processing-convenient percentile-thresholding strategy can be selected to overcome this inconvenience (Wang et al., 2008).
is selected as the th largest absolute value among all values in the transformed domain, where the predefined percentile threshold such that
. Here, returns percentile of the values in