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I doubt that compressed sensing will be very effective for this problem. Many of the guarantees for compressive signal recovery require incoherence between mea
by lp251 12y ago
I doubt that compressed sensing will be very effective for this problem. Many of the guarantees for compressive signal recovery require incoherence between measurements- meaning each measurement is sufficiently different from the others. In this case, each measurement is highly correlated with the others.
The Rice single pixel camera (discussed on the wiki page) effectively multiplies the image by a random mask before it is sensed by the photodiode. This is how they control the incoherence property.
- greendestiny 12y agoYou might technically correct in the limited sense that this isn't a 'compressive' sensing - but it's an absolutely classical example of sparse reconstruction. You can resample that radon transformed image randomly and reconstruct it as a sparse fourier image. There is matlab code out there if you google around a bit.
- thwest 12y agoCompressive Sensing using the Radon transform associated with radar has extensive literature. Not sure about the OPs imager. The optimization techniques are applicable to most sparse signal reconstruction transforms. Formally you would look to show the Restricted Isometery Property. http://users.ece.gatech.edu/~justin/ECE-8823a-Spring-2011/Resources_files/RandomConvolution-final-Aug09.pdf http://users.ece.gatech.edu/~justin/ECE-8823a-Spring-2011/Re...
- greendestiny 12y agoIt's a dense sensing of the radon transform - hence its not compressive. But you can resample that lots of ways and satisfy the RIP. Reconstruction of images from sparse radon transforms is one of the early examples that helped shape the field.
- lp251 12y agoSure- admittedly, confusing "sparse reconstruction" with "compressed sensing" is a pet peeve of mine.