# Two-Dimensional Linear Inversion of GPR Data with a Shifting Zoom along the Observation Line
## 6 Conclusions  
In this study, a shifting zoom method was proposed, in order to enable the application of a linear inversion to a long radar image, without suffering from negative effects essentially due to a limited view angle, introduced by the subdivision of the image into smaller subdomains. The shifting zoom extends the method introduced in [29]. Relative to [29], the improvement achieved by the shifting zoom is that the vertical stitches disappear completely, whereas in that work their number was two-fold larger than with adjacent investigation domains. This is due to the fact that the central belt is quite narrow relative to the entire current investigation domain, whereas it was as large as half of the investigation domain in [29]. Consequently, in that case there was a meaningfully different average level between any two adjacent final images. Moreover, under the method explained in [29], the length of the observation line, in general, was not an integer multiple of the width of the chosen investigation domain, and some cases, dependent \"manual binding\" or zero padding was needed, in order to stitch together the entire data gathered along the observation line. With a shifting zoom, the settings of a number of inversions that guarantee the entire coverage of the gathered observation line can be easily made automatic, and do not require any zero-padding. That said, the different (certainly superior) quality of the results achieved here are also due the larger band of the antennas, the more controlled environmental conditions and the fact that the targets were shallower. The extra computational burden needed for the shifting zoom with respect to the use of adjacent investigation domains is minimal, because the matrix to be inverted is calculated completely off-line, as is its SVD. What is needed when performing the shifting zoom, is a larger number of matrix-vector products that are fast operators. In particular, calculation of the elements of the matrix and computation of its numerical SVD requires slightly less than two hours, whereas the sequential shifting zoom requires about 30 s. This is the extra time needed in the case at hand. When an extrapolation to possible real-life cases is performed, this means that considering, for example, 60 B-scans, each of which is 24 m long (which means 10 times the B-scan considered here) the time specifically needed for the shifting zoom would be in the order of 30 \(\times\) 10 \(\times\) 60 s = 18,000 s = 5 h. This may correspond, for example, to the size of an area of archaeological interest which needs to be probed. The inversion also required some work on the data (inverse Fourier transform in time domain, zero timing, background removal, time cut, Fourier transform again--because the inversion is in the frequency domain), but the required CPU time for this was shorter than 30 s and would not increase meaningfully on larger scales. So, most of the required computational time was devoted to the calculation of the matrix and its SVD, which is the same, either with or without, shifting zoom. Please note that due to the limited available RAM memory, it was impossible to perform a SVD of the matrix corresponding to the entire investigation and observation domains (2.4 m long) with the available computer, which was an ASUS desktop with 2 Gb of RAM. It is worth noting that also a migration is, in general, expressed as an integral weighted summation of the data around a central point, and this means also that a migration, if examined more attentively, is implicitly based on a shifting zoom algorithm. In conclusion, this work proposes a translation in the plane of inversion for a procedure customarily applied to migration algorithms. Future research works will focus on further real radar datasets, possibly on larger scales, to combine the proposed method with the intrinsic, near-field antenna model of [PERSON] and [PERSON] [39; 40], through which antenna effects will be further filtered out.