## 3 Archaeological Feature Extraction from SAR: Methodological Approaches
### Multi-Temporal Analysis  
Multi-temporal studies are mainly based on co-registration, speckle filtering, stacking averaging, multi-temporal surveillance consisting of steps of SAR image visual inspection, Gaussian filtering, and ratio change detection (see Figure 1). In order to cover the growth cycle of plants, multi-temporal SAR data acquired with similar imaging geometries (_i.e._, repeat cycle) are preferred. In this study (see Table 1), 40 COSMO-SkyMed images, acquired in 2013, were used. For the purpose of multi-temporal analysis, the datasets were co-registered with sub-pixel accuracy in three steps: (1) a first shift is initialized using the satellite orbital parameters; (2) the shift estimation is enhanced (sub-pixel accuracy) by means of a cross-correlation-based function using a grid of image windows; (3) the final shift is further refined by using over-sampled data. Figure 2: Single data procedure for the enhancement of archaeological marks. Note that the preprocessing for Spotlight images (for additional details see [29]) upgrades raw data (level 0) to Geocoded Terrain Corrected (GTC) data, namely level 1d product, by means of four steps. The first processing step aims (to obtain Level 1A product) at generating Single-look Complex Slant (SCS) products by means of internal calibration and data focusing. In the second step image detection (amplitude), ellipsoid ground projection and statistics evaluation are performed. The last two steps consists on generating Geocoded Ellipsoid Corrected products (level 1C) and Geocoded Terrain Corrected products (level 1D). Speckle, an unfavorable noise that suppresses feature signals, usually occurs in SAR images due to the coherent nature of the system. Speckle noise reduction is beneficial for archaeological feature extraction. There are several speckle filtering algorithms, including the Lee filter [30], the Lee enhanced filter [31] and the Frost and Kuan filters [32], _etc._ The performance of an algorithm is evaluated from speckle suppression together with topology preservation, because the presence of geometric features, being quite rare in nature, generally implies signs of archaeological sites and human activity in the distant past. In this study, the enhanced Lee approach [31] was applied as a trade-off between filtering performance and robustness. For co-registered SAR images, the stacking averaging is helpful in mitigating speckle noise by increasing the Equivalent Number of Looks (ENL). Assuming \(N\) co-registered images are available, the ENL of the derived stacking-averaged SAR image would be enhanced by a factor of \(\sqrt{N}\). In such a way, weak archaeological features hidden in a single SAR image could become prominent, particularly for the shadow marks (_i.e._, microrelief) showing consistent phenomena in all acquisitions. Consequently, the stacking averaging is beneficial for enhancing shadow marks in archaeology using SAR images. In multi-temporal observation, visual inspection is firstly used to identify regular patterns that generally characterize cultural features. Due to the coherent nature of imaging, archaeological features in a single SAR image may be ambiguous and require feature enhancement techniques. In this study, Gaussian filter and ratio change detection were applied. The Gaussian filter is often used in geometric feature enhancement. Mathematically, it modifies the input signal by convolution with a Gaussian function and uses weighting from the probability density function. This filtering is particularly efficient in reducing speckle noise, preserving radar reflectivity and textural properties. Experiments in our study proved that this filter is useful to discriminate archaeological signs (crop, soil and damp anomalies) from their surroundings in SAR images. Although multi-temporal SAR images are available, archaeological anomalies are always prominent in one or two acquisitions. The ratio between two data enables us to enhance the difference between the \"anomaly\" linked to buried-archaeological structures and their surroundings.