1. A method of creating an image from an initial data set, the method comprising: receiving the initial data set, the receiving comprising receiving data representing transmission site locations of radar pulses applied into ground in a ground penetrating radar application, reception site locations of reception of reflections from the radar pulses, radar-return profiles for pairings of the transmission site locations and the reception site locations, and data samples associated with individual radar-return profiles; processing the initial data set with a processing device by creating an estimated image value for each voxel in the image to create an estimated image value data set having most of the estimated image value data set's values at or near zero by iteratively deriving the estimated image value through application of a majorize-minimize principle to solve an l 1 -regularized least-squares estimation problem associated with a mathematical model of image data from the initial data set; displaying the image using the estimated image value of individual voxels of the image.