Data Enhancement via Low-Rank Matrix Reconstruction in Pulsed Thermography for Carbon-Fibre-Reinforced Polymers

Pulsed thermography is a commonly used non-destructive testing method and is increasingly studied for the assessment of advanced materials such as carbon fibre-reinforced polymer (CFRP). Different processing approaches are proposed to detect and characterize anomalies that may be generated in structures during the manufacturing cycle or service period. In this study, matrix decomposition using Robust PCA via Inexact-ALM is investigated as a pre- and post-processing approach in combination with state-of-the-art approaches (i.e., PCT, PPT and PLST) on pulsed thermography thermal data. An academic sample with several artificial defects of different types, i.e., flat-bottom-holes (FBH), pull-outs (PO) and Teflon inserts (TEF), was employed to assess and compare defect detection and segmentation capabilities of different processing approaches. For this purpose, the contrast-to-noise ratio (CNR) and similarity coefficient were used as quantitative metrics. The results show a clear improvement in CNR when Robust PCA is applied as a pre-processing technique, CNR values for FBH, PO and TEF improve up to 164%, 237% and 80%, respectively, when compared to principal component thermography (PCT), whilst the CNR improvement with respect to pulsed phase thermography (PPT) was 77%, 101% and 289%, respectively. In the case of partial least squares thermography, Robust PCA results improved not only only when used as a pre-processing technique but also when used as a post-processing technique; however, this improvement is higher for FBHs and POs after pre-processing. Pre-processing increases CNR scores for FBHs and POs with a ratio from 0.43% to 115.88% and from 13.48% to 216.63%, respectively. Similarly, post-processing enhances the FBHs and POs results with a ratio between 9.62% and 296.9% and 16.98% to 92.6%, respectively. A low-rank matrix computed from Robust PCA as a pre-processing technique on raw data before using PCT and PPT can enhance the results of 67% of the defects. Using low-rank matrix decomposition from Robust PCA as a pre- and post-processing technique outperforms PLST results of 69% and 67% of the defects. These results clearly indicate that pre-processing pulsed thermography data by Robust PCA can elevate the defect detectability of advanced processing techniques, such as PCT, PPT and PLST, while post-processing using the same methods, in some cases, can deteriorate the results.

Robust Principal Component Thermography for Defect Detection in Composites

Pulsed Thermography (PT) data are usually affected by noise and as such most of the research effort in the last few years has been directed towards the development of advanced signal processing methods to improve defect detection. Among the numerous techniques that have been proposed, principal component thermography (PCT)—based on principal component analysis (PCA)—is one of the most effective in terms of defect contrast enhancement and data compression. However, it is well-known that PCA can be significantly affected in the presence of corrupted data (e.g., noise and outliers). Robust PCA (RPCA) has been recently proposed as an alternative statistical method that handles noisy data more properly by decomposing the input data into a low-rank matrix and a sparse matrix. We propose to process PT data by RPCA instead of PCA in order to improve defect detectability. The performance of the resulting approach, Robust Principal Component Thermography (RPCT)—based on RPCA, was evaluated with respect to PCT—based on PCA, using a CFRP sample containing artificially produced defects. We compared results quantitatively based on two metrics, Contrast-to-Noise Ratio (CNR), for defect detection capabilities, and the Jaccard similarity coefficient, for defect segmentation potential. CNR results were on average 40% higher for RPCT than for PCT, and the Jaccard index was slightly higher for RPCT (0.7395) than for PCT (0.7010). In terms of computational time, however, PCT was 11.5 times faster than RPCT. Further investigations are needed to assess RPCT performance on a wider range of materials and to optimize computational time.

Robust PCA via Regularized Reaper with a Matrix-Free Proximal Algorithm

Principal component analysis (PCA) is known to be sensitive to outliers, so that various robust PCA variants were proposed in the literature. A recent model, called reaper, aims to find the principal components by solving a convex optimization problem. Usually the number of principal components must be determined in advance and the minimization is performed over symmetric positive semi-definite matrices having the size of the data, although the number of principal components is substantially smaller. This prohibits its use if the dimension of the data is large which is often the case in image processing. In this paper, we propose a regularized version of reaper which enforces the sparsity of the number of principal components by penalizing the nuclear norm of the corresponding orthogonal projector. If only an upper bound on the number of principal components is available, our approach can be combined with the L-curve method to reconstruct the appropriate subspace. Our second contribution is a matrix-free algorithm to find a minimizer of the regularized reaper which is also suited for high-dimensional data. The algorithm couples a primal-dual minimization approach with a thick-restarted Lanczos process. This appears to be the first efficient convex variational method for robust PCA that can handle high-dimensional data. As a side result, we discuss the topic of the bias in robust PCA. Numerical examples demonstrate the performance of our algorithm.

Fingerprint Database Reconstruction Based on Robust PCA for Indoor Localization

The indoor localization method based on the Received Signal Strength (RSS) fingerprint is widely used for its high positioning accuracy and low cost. However, the propagation behavior of radio signals in an indoor environment is complicated and always leads to the existence of outliers and noises that deviate from a normal RSS value in the database. The fingerprint database containing outliers and noises will severely degrade the performance of an indoor localization system. In this paper, an approach to reconstruct the fingerprint database is proposed with the purpose of mitigating the influences of outliers. More specifically, by exploiting the spatial and temporal correlations of RSS data, the database can be transformed into a low-rank matrix. Therefore, the RPCA (Robust Principle Component Analysis) technique can be applied to recover the low-rank matrix from a noisy matrix. In addition, we propose an improved RPCA model which takes advantage of the prior knowledge of a singular value and could remove outliers and structured noise simultaneously. The experimental results show that the proposed method can eliminate outliers and structured noise efficiently.

Consistent metagenomic biomarker detection via robust PCA

BACKGROUND

Recent developments of high throughput sequencing technologies allow the characterization of the microbial communities inhabiting our world. Various metagenomic studies have suggested using microbial taxa as potential biomarkers for certain diseases. In practice, the number of available samples varies from experiment to experiment. Therefore, a robust biomarker detection algorithm is needed to provide a set of potential markers irrespective of the number of available samples. Consistent performance is essential to derive solid biological conclusions and to transfer these findings into clinical applications. Surprisingly, the consistency of a metagenomic biomarker detection algorithm with respect to the variation in the experiment size has not been addressed by the current state-of-art algorithms.

RESULTS

We propose a consistency-classification framework that enables the assessment of consistency and classification performance of a biomarker discovery algorithm. This evaluation protocol is based on random resampling to mimic the variation in the experiment size. Moreover, we model the metagenomic data matrix as a superposition of two matrices. The first matrix is a low-rank matrix that models the abundance levels of the irrelevant bacteria. The second matrix is a sparse matrix that captures the abundance levels of the bacteria that are differentially abundant between different phenotypes. Then, we propose a novel Robust Principal Component Analysis (RPCA) based biomarker discovery algorithm to recover the sparse matrix. RPCA belongs to the class of multivariate feature selection methods which treat the features collectively rather than individually. This provides the proposed algorithm with an inherent ability to handle the complex microbial interactions. Comprehensive comparisons of RPCA with the state-of-the-art algorithms on two realistic datasets are conducted. Results show that RPCA consistently outperforms the other algorithms in terms of classification accuracy and reproducibility performance.

CONCLUSIONS

The RPCA-based biomarker detection algorithm provides a high reproducibility performance irrespective of the complexity of the dataset or the number of selected biomarkers. Also, RPCA selects biomarkers with quite high discriminative accuracy. Thus, RPCA is a consistent and accurate tool for selecting taxanomical biomarkers for different microbial populations.

REVIEWERS

This article was reviewed by Masanori Arita and Zoltan Gaspari.