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We apply compressive sensing to reconstruct a signal if it is sparse in the original domain or has a sparse represetation in some basis.

  1. How we may know a if a signal is sparse or has a sparse represetation ?
  2. Is a radar received signal sparse or has a sparse representation ?
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It depends on the application and on what basis you decide to look at. If there are only a few targets and little to no clutter, then a radar image can be considered sparse in the image domain i.e. it has only a few Fourier components. A possible example of this is ground to air or air to air radars.

Synthetic Aperture Radar (SAR) imaging of the ground - imaging point-like targets on a specular reflecting surfaces (road, highways, airport runways) may also be considered sparse in the image domain. Once you have speckle though (e.g. high res imaging of fields, trees etc) then the image is not sparse in the target domain and sparse reconstruction will have a hard time with this type of data. The spare reconstruction may be able to separate point like targets from the clutter because it reconstructs the targets and not the speckle background.

Sparse reconstruction has also been applied to Inverse-SAR imaging of ships at sea. The ship tends to behave as a collection of corner or other simple reflectors - the reflection off the ocean waves tends to be away from the radar. You do run into cases where the ocean surface is rough and you get significant returns from it.

Yet another approach in SAR imaging to assume that the gradient of the image is sparse. This tends to behave like an edge detector.

So, it really depends on the application of the radar and on what basis you decide to use.

The CoSeRa workshop is held almost every year and focuses on compressive sensing. Many of the papers are focused on radar applications (SAR, moving target indication, tomography). The papers from the last few years are available through the IEEE.

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  • $\begingroup$ when we use the radar for automotive applications such blind spot detection, ACC, line assistant change.. and we would like to reconstruct the range-doppler map here we may suppose that we have a few number of targets and then we have a sparse representation ! so what's the name of this domain (basis) ? $\endgroup$ – Issa Jul 10 '18 at 15:13
  • $\begingroup$ If you are assuming that the targets are sparse - then I would start there and build you signal model based on the type of signal processing you are doing. You can do the sparse estimation on pulse compressed or non-pulse compressed data. Are you doing standard pulse compression or stretch processing? These are what you have to answer for your own application. Sometimes the sparse reconstruction works well in one domain but not in another, so you may have to experiment doing it in the time-domain or frequency domain and in both range and cross range dimensions. $\endgroup$ – David Jul 10 '18 at 19:20
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As the other answer said,it depends on your application and your target specification. I would suggest to take raw data (if you have the radar, or simulate the target) and start analysis by transforming into Fourier or wavelet domain. Submit the results here for further discussion

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