Delay-and-sum algorithms are imaging techniques in nondestructive testing, which form images by summing backpropagated signals. Under this approach, a small number of high-intensity signals, such as those from boundary reflections, may create artifacts that degrade the image and hinder defect detection. This article introduces a probabilistic model of the summation, which explains the origin of this effect and proposes to replace the summation in the imaging algorithm by the more statistically robust geometric median. As demonstrated on an experimental inspection using multiview total focusing method and plane wave imaging, this novel technique effectively suppresses some artifacts, at the expense of an increase in the structural noise amplitude and additional diffraction artifacts at the ends of some structural features. As such, the geometric median provides an alternative imaging approach that may improve the performance in some circumstances.