Radar and filters

Although I've been working remotely, the door to the lab I work in on campus (which also is home to my office) expressly labels the lab a radar lab. Yet, despite that conspicuous label and all the exciting radar research going on around me, I had extremely little acquaintance with radar data until my current project. One component of that project is examining the time evolution of the 2014-2015 Holuhraun volcanic eruption. Much of this eruption's activity occurred in the winter of 2014, during which the flow field was often shrouded in long arctic nights. Radar, rather than visible imaging, is thus an excellent resource to examine this period of activity. I am specifically using data from the Sentinel 1 satellites.

Coming from a background in high-resolution visible imagery, especially the High-Resolution Imaging Science Experiment (HiRISE) camera that orbits Mars, I found the "static" in radar data to be particularly annoying. This phenomenon is more precisely called speckle and is often thought of as noise, though strictly, noise is usually understood to mean contamination of a signal whereas speckle is part of the signal that arises due to surface roughness at smaller scales than the radar wavelength (3.75-7.5 cm in this case).

A variety of techniques have been developed to reduce speckle. These may be divided into non-adaptive and adaptive filters. Non-adaptive filters use the same weighting across an entire image whereas adaptive filters vary their weightings based on local speckle level. The simplest filters calculate the mean or median and are non-adaptive. They are especially poor at preserving edges. The Lee filter is a commonly used traditional adaptive filter and (skipping much math) minimizes the mean squared error relative to a linearized model. The result is that homogeneous areas are aggressively smoothed whereas highly heterogenous areas, such as edges, are unfiltered in order to preserve detail. 

In my particular case, I am mapping the evolving margins of the Holuhraun flow field. Therefore, the non-adaptive filters blur my target whereas the Lee filter introduces a somewhat jarring discrepancy between the smoothed interior of the flow and its unfiltered margin. Moreover, after Lee filtering, the smoothed interior looks something like a patchwork corduroy cloud (also seen in the mean filter), which isn't realistic. Poking around a bit online, I found a general use filter called a bilateral filter (though it has been used to despeckle radar data as well). This filter calculates the weighted average of each neighborhood of pixels, where the weighting depends on both the distance of the pixel and the difference of the pixel (that is, how much brighter or darker the pixel is than the reference pixel at the center). The result once again is that homogeneous areas are despeckled and edges left unfiltered, but the filtering is sufficiently consistent to avoid both the jarring "seam" at the margins and the patchwork smoothing of the interior produced by the Lee filter. After some experimenting, I found that the bilateral filter cued my eyes to subtle differences that were there in the original data but not easily recognizable due to the speckle.

There is a caveat to using the filters I've described. Although they "clean up" the data, they do so with neither knowledge nor direct modeling of the underlying cause of the speckle, namely, roughness below the radar wavelength. The result is an image that humans, and computers, can more easily interpret but, in effect, that filtered image itself is an interpretation. By comparison, a state-of-the-art algorithm developed by Antoine Lucas takes a step toward considering fine-scale roughness, albeit implicitly. This algorithm models the probability that two adjacent neighborhoods of pixels each have the same "true" (speckle-less) value. By combining many such estimations, speckle can be significantly reduced. Antoine developed this algorithm specifically to facilitate interpretation of radar images of Saturn's moon Titan captured by the Cassini spacecraft. The results (example below) are very impressive!