High-speed rail (HSR) requires high levels of reliability of the track infrastructure.  Automated visual inspection is useful for finding many anomalies such as cracks or chips on joint bars and concrete ties, but existing vision-based inspection systems often produce high number of false detections, and are very sensitive to external factors such as changes in environmental conditions.  For example, state-of-the-art algorithms used by the railroad industry nominally perform at a detection rate of 85% with a false alarm rate of 3% and performance drops very quickly as image quality degrades.  On the tie inspection problem, this false alarm rate would correspond to 2.6 detections per second at 125 MPH, which cannot be handled by an operator.  These false detections have many causes, including variations in anomaly appearance, texture, partial occlusion, and noise, which existing algorithms cannot handle very well.  To overcome these limitations, it is necessary to reformulate this joint detection and segmentation problem as a Blind Source Separation problem, and use a generative model that is robust to noise and is capable of handling missing data.

In signal and image processing, Sparse Representations (SR) is an efficient way of describing a signal as a linear combination of a small number of atoms (elementary signals) from a dictionary.  In natural images, sparsity arises from the statistical dependencies of pixel values across the image.  Therefore, statistical methods such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Independent Component Analysis (ICA) have been used for dimensionality reduction in several computer vision problems.  Recent advances in SR theory have enabled methods that learn optimal dictionaries directly from training data.  For example, K-SVD is a very well known algorithm for automatically designing over-complete dictionaries for sparse representation.

In this detection problem, the anomalies have very well defined structure and therefore, they can be represented sparsely in some subspace.  In addition, the image background has very structured texture, so it is sparse with respect to a different frame.  Theoretical results in mathematical geometric separation show that it is possible to separate these two image components (regular texture from contours) by minimizing the L1 norm the coefficients in geometrically complementary frames.  More recently, it has been shown that this problem can be solved efficiently using thresholding and total variation regularization.  Our experiments show that the sparse coefficients extracted from the contour component can be converted into feature vectors that can be used to cluster and detect these anomalies.