Dr Ludger Prünte from Fraunhofer Institute for High Frequency Physics and Radar Techniques (FHR), Germany, talks to Electronics Letters about his paper ‘SAR imaging from incomplete data using elastic net regularisation’, page 1667. Ludger Prünte The main aspect of my work is the application of modern, regularisation-based signal processing methods to airborne, pulsed radar data. In contrast to classical methods, in my work I do not apply filtering. Instead, due to my background in industrial mathematics, I compute the underlying scenery from the underdetermined data using a side condition, which varies with intended application. My main research interest is detecting moving vehicles on the ground using multichannel data. Since moving vehicles are sparsely distributed over the scenery, this can be achieved by employing a sparsity-inducing regulariser and using compressed sensing. Nevertheless, the broad scope of my department at the Fraunhofer Institute gives me the exciting opportunity to apply my methods in related fields like synthetic aperture radar (SAR). We are currently witnessing developments towards achieving cognitive radar. This achievement would result in an autonomous choice of the current radar mode and enable multifunctional use of the radar antenna. Tasks with long periods of antenna occupation, such as SAR, impede this progress. However, omitting pulses, randomly distributed or arranged contiguously, allows an interlaced operation with multiple radar modes, as well as dealing with single pulses corrupted by interference. In order to obtain valuable signal-to-noise ratio, a high density of pulses is necessary. Consequently, we are not aiming to reduce the pulse repetition frequency (PRF) to the Nyquist rate, but rather we are aiming to compute the SAR image from data with high PRF with randomly missing pulses. This technique is also known as interrupted SAR. Unfortunately, classical SAR imaging approaches are not able to focus such data correctly, resulting in strong band-shaped artefacts. There are two classical approaches to handle omitted pulses. Firstly, the missing pulses can be interpolated from neighbouring pulses and a classical SAR image is computed afterwards. Secondly, the SAR image can be reconstructed using compressed sensing. The latter is well known for its stability against missing data, but it enforces sparsity in the SAR image, even if the scenery is dense. To overcome this, in my Letter I have complemented the regulariser according to the “elastic net” approach. This approach allows to image sparse features of the scenery, such as strong single scatterers, as well as dense features such as forests. As presented in my Letter, the elastic net approach significantly reduces the artefacts in the SAR image induced by missing pulses. In the reported work, only single, randomly-chosen pulses have been omitted. Nevertheless, this gives the option to neglect data affected by interference or to use the radar antenna for other purposes, such as communications, at the same time as recording data for a good quality SAR image. In comparison to a classical filter-based SAR imaging, applying the elastic net approach to a full dataset increases the SNR of the image. Elastic net regularisation is well known in several different fields of data analysis. From a mathematical point of view, although the structure of the imaged “scenery” is quite different, the structure of the measurement process for SAR data is quite similar to that of seismic exploration or magnetic resonance imaging. Hence, a fruitful exchange of methods should be possible. Additionally, this work offers a starting point for increasing the flexibility of cognitive radar steering by reducing the limitations induced by SAR recording. My Letter in this issue of Electronics Letters shows the case of single, randomly-chosen omitted pulses. I am currently working on enhancements to deal with the case of missing groups of consecutive pulses. These would give the option to interlace the recording of the SAR data with GMTI. Moreover, the parameterisation of the elastic net approach needs to be analysed from a theoretical point of view. I expect that these insights will allow a better reconstruction. Nevertheless, I am not convinced that the elastic net approach is the optimum regulariser for every type of scenery. Hence, I have identified alternative regularisers that might be more suitable in some cases and I am eager to see the results. Nine years ago I started working in the field of signal processing for airborne radar. At this time filtering was the basis of almost all approaches. Nowadays, regularisation-based approaches are more often taken into account, partly inspired by the emergence of compressed sensing. For the future, I would predict that both approaches will have impact, as a flexible choice of methods will be imperative. I believe that this integration of methods will be enforced by the development of a cognitive radar- and also by the trend towards multi-static measurement devices with variable geometry.
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Oct 31, 2018
Brandon Ravenscroft + 5
Open Access
