Non parametric methods for multidimensional wavefront estimation

In active remote sensing applications the time of delay (or phase) of backscattered wavefield recorded by arrays of sensors is useful to get information about the target and/or the propagating medium. The authors propose two methods for non-parametric estimation of the time of delay (or phase) function. Both methods are suitable for the wavefront estimation when the arrangement of sources and receivers are rather complex and non-regularly spaced. In addition, the estimate is carried out simultaneously on the (n+1)-dimensional the space of measurements (n⩾1) thus avoiding the extraction of lower dimensional subsets. Examples from SAR interferometry and reflection seismology demonstrate the potentialities of the methods.