Imaging the earth's interior
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Use of the Hough transformation to detect lines and curves in pictures
Communications of the ACM
Detection of linear objects in GPR data
Signal Processing
Using the generalized Radon transform for detection of curves in noisy images
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 04
Sparse Signal Reconstruction from Noisy Compressive Measurements using Cross Validation
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Feature detection algorithms in computed images
Feature detection algorithms in computed images
A compressive sensing data acquisition and imaging method for stepped frequency GPRs
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Reconstruction From Noisy Random Projections
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Compressed Sensing and Redundant Dictionaries
IEEE Transactions on Information Theory
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Feature detection in sensing problems usually involves two processing stages. First, the raw data collected by a sensor, such as a Ground Penetrating Radar (GPR), is inverted to form an image of the subsurface area. Second, the image is searched for features like lines using an algorithm such as the Hough Transform (HT), which converts the problem of finding spatially spread patterns in the image space to detecting sparse peaks in the HT parameter space. This paper exploits the sparsity of features to combine the two stages into one direct processing step using Compressive Sensing (CS). The CS framework finds the HT parameters directly from the raw sensor measurements without having to construct an image of the sensed media. In addition to skipping the image formation step, CS processing can be done with a minimal number of raw sensor measurements, which decreases the data acquisition cost. The utility of this CS-based method is demonstrated for finding buried linear structures in both simulated and experimental GPR data.