KEYWORDS: Data modeling, Wave propagation, Diagnostics, Data acquisition, Principal component analysis, Inspection, Nondestructive evaluation, Scattering, Velocity measurements, Data processing
This work investigates the problem of anomaly detection by means of an agnostic inference strategy based on the concepts of spatial saliency and data sparsity. Specifically, it addresses the implementation and experimental validation aspects of a salient feature extraction methodology that was recently proposed for laser-based diagnostics and leverages the wavefield spatial reconstruction capability offered by scanning laser vibrometers. The methodology consists of two steps. The first is a spatiotemporal windowing strategy designed to partition the structural domain in small sub-domains and replicate impinging wave conditions at each location. The second is the construction of a low-rank-plus-outlier model of the regional data set using principal component analysis. Regions are labeled salient when their behavior does not belong to a common low-dimensional subspace that successfully describes the typical behavior of the anomaly-free portion of the surrounding medium. The most at tractive feature of this method is that it requires virtually no knowledge of the structural and material properties of the medium. This property makes it a powerful diagnostic tool for the inspection of media with pronounced heterogeneity or with unknown or unreliable material property distributions, e.g., as a result of severe material degradation over large portions of their domain.
Compressive sampling (CS), or Compressed Sensing, has generated a tremendous amount of excitement in the signal processing community. Compressive sampling, which involves non-traditional samples in the form of randomized projections, can capture most of the salient information in a signal with a relatively small number of samples, often far fewer samples than required using traditional sampling schemes. Adaptive sampling (AS), also called Active Learning, uses information gleaned from previous observations (e.g., feedback) to focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional (non-adaptive) sampling schemes. This paper compares the theoretical performance of compressive and adaptive sampling for regression in noisy conditions, and it is shown that for certain classes of piecewise constant signals and high SNR regimes both CS and AS are near optimal. This result is remarkable since it is the first evidence that shows that compressive sampling, which is non-adaptive, cannot be significantly outperformed by any other method (including adaptive sampling procedures), even in the presence of noise. The performance of CS schemes for signal detection is also investigated.
Compressive Sampling, or Compressed Sensing, has recently generated
a tremendous amount of excitement in the image processing community. Compressive Sampling involves taking a relatively small number of non-traditional samples in the form of projections of the signal onto random basis elements or random vectors (random projections). Recent results show that such observations can contain most of the salient information in the signal. It follows that if a signal is compressible in some basis, then a very accurate reconstruction can
be obtained from these observations. In many cases this reconstruction is much more accurate than is possible using an equivalent number of conventional point samples. This paper motivates the use of Compressive Sampling for imaging, presents theory predicting reconstruction error rates, and demonstrates its
performance in electronic imaging with an example.
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