Compressive sensing of parameterized shapes in images

Compressive sensing (CS) uses a relatively small number of non-traditional samples in the form of randomized projections to reconstruct sparse or compressible signals. The Hough transform is often used to find lines and other parameterized shapes in images. This paper shows how CS can be used to find parameterized shapes in images, by exploiting sparseness in the Hough transform domain. The utility of the CS-based method is demonstrated for finding lines and circles in noisy images, and then examples of processing GPR and seismic data for tunnel detection are presented.