Guided Wave Structural Health Monitoring, GWSHM, involves exciting high frequency mechanical waves in plate, beam, or rod-like structures and sensing the scattered response in order to detect, localize, and characterize damage. Through a process of phase-coherent delay-weight-sum similar to that used in some sonar and radar applications, time-domain scattered responses measured at several closely spaced discrete piezoelectric array elements can be transformed into a single two-dimensional signal representation of amplitude (usually strain or voltage) versus distance and look direction. In this two dimensional representation, a single waveform pulse scattered from a single damage target has a predictable approximate shape which is a function of the pulse wavelength and window, and the geometric layout of the sensing array. The full response of an array, including all primary and secondary reflections (or echoes) from damage, can then be approximated by a superposition of shape functions corresponding to a finite set individual scatter targets. In this paper, following a review of the spatial domain transformation process, we describe how one can estimate the amplitude, arrival time, and bearing (arrival direction) of each discrete target through matching pursuit.