SOFA radargram enhancement and target physical slope estimation

If you already read the SOFA's short sad story, you already know that SOFA may provide some (hopefully) useful and innovative results which may deserve to be published some day. In the meanwhile, I report some of the results and images that have been unsuccessfully submitted for review in 2017, which may lead to some new cool idea in somebody else's brain. I will be happy to be involved in the development of such new ideas, for sure!
The ideas reported in this page have been tested on SHARAD data. However, the general concepts can be extended also to other radar sounders, also airborne ones.

Practical example: a little sample python3 program that allows the creation of the images reported later on this page is available here.

Index

Multiple squinted short-aperture radargrams
Radargram enhancement
Target slope estimation
Directional multilooking
Further analyses

Multiple squinted short-aperture radargrams

Using SOFA it is possible to generate squinted radargrams using short apertures. Singularly, each radargram will have a low visual quality, but it will enhance targets that are perpendicularly oriented with respect to the squint angle. Such targets will have a better SNR in the squinted images with respect to the standard processed one. This concept is clear in the following images (note: all the images shown in this page have been normalized and thresholded according to their average noise power, so they are all comparable).

SHARAD radargram 371502, standard processing	Squint = 0º, aperture approx 1º
Squint = -0.5º, aperture approx 1º	Squint = 0.5º, aperture approx 1º

Radargram enhancement

As mentioned before, each squinted radargram highlights the targets which have a physical slope perpendicular to the viewing squint angle. If the radargram is processed using subsequent squinted small apertures, this property can be exploited by properly combining them and assigning to the enhanced radargram sample the maximum power recorded on the squint images. In my proposal, this was summarized as follows:

where:
N is the number of equally-spaced small squinted apertures,
P(i,j,theta_k) is the power of the radargram sample (i,j) for the squint angle theta_k,
P_hat(i,j) is the new power calculated for the radargram sample (i,j),
g_theta represents a 1D Gaussian smoothing operator with fixed standard deviation sigma_theta.
For specular reflectors, this solution allows for a certain amount of multilooking. At the same time, it avoids the inclusion in the averaging of squint angles where noise is dominant. This better preserves the scattering power of targets. Examples of radargram details obtained using the proposed combination approach are shown in the following images. The enhanced radargram has been obtained combining N = 61 subapertures approximately 1º wide and spanning from -1.5º to 1.5º squint angles. As the images show, this combination enhances subsurface targets and especially sloped targets, which greatly benefit from the squinted processing.

Detail 1, standard processing	Detail 1, max-processed
Detail 2, standard processing	Detail 2, max-processed

Target slope estimation

Besides selecting the maximum power for radargram enhancement, from P(i,j,theta_k) it is also possible to detect the Direction of Maximum Scattering (DMS) of targets. The DMS is equal to the squint angle theta_k corresponding to the maximum sample power, as follows:

The DMS is directly related to the slope of targets. For the SHARAD geometry, DMS could be a good direct approximation of target physical slopes. In the case of airborne sounders, however, further calculations are necessary to convert the DMS into target physical slopes, as refraction indexes and ray bending become not negligible. An example of DMS map is reported in the following. The pixels below a threshold calculated using a probability of false alarm of 10^-3 have been masked.

DMS map / estimation of target physical slopes

Directional multilooking

Using the DMS information it is possible to perform directional multilooking using the target slope physical information. Before, it is necessary to transform the physical domain slopes into image domain slopes. This can be accomplished with the following equation:

where delta_alt and delta_r are the radargram along-track and range spacing, respectively.

Directional multilooking can be obtained by using uniform or Gaussian filters locally rotated according to the corresponding DMS. Such directional averaging greatly preserves sloped targets and allows, at the same time, to benefit from reduced noise. Examples of results obtained with an uniform filter of size N_avg = 5 are reported in the following image.

Standard along-track averaging (left) vs. directional averaging (right) using an uniform filter of size N_avg = 5.

Further analyses

Using the information coming from squinted processing, it is also possible to estimate other measurements. As a further example, the analysis of the width of the beam of target power in the squint dimension can provide information about the roughness of the target itself. Other measurements are possible. If you are interested, just ask. I have a lot of material! :)