Hyperspectral Infrared Imaging
--- B. Yousefi's second Ph.D. in Computational methods for Infrared, Department of Electrical and Computer Engineering, Laval University. ---
Matrix factorization techniques can effectively detect defects in sequence of thermal images. Some well-known matrix factorization methods, such as principal component analysis/thermography (PCA/PCT) and non-negative matrix factorization (NMF), have been used for past several years in different fields. However, the major challenge of dealing with non-negative high-dimensional infrared imaging sequences in different applications persists. In this research, we propose difference low-rank matrix approximation methods to two different scenarios through active and passive thermographical imaging.
After using PCT to detect thermal defects, several other alternative approaches have been used to modify the PCT such as, incremental PCT, or candid covariance-free incremental PCT (CCIPCT); these approaches modified PCT by updating a fixed set of basis, making it incremental algorithm, and surpassing the covariance calculation, respectively. Sparse- PCT, and sparse matrix analysis increase the sparsity in the analyses and strengthening the important bases by adding regularization terms. This mitigates noise for detecting defective patterns. The reconstruction of input thermal sequence involves a combination of negative and positive bases due to lack of restriction in extracting bases and coefficients in PCT, which might cause overlapping among the distinct basis in low-rank matrix approximation.
Non-negative matrix factorization (NMF) is a matrix factorization technique similar to PCA and has additive constraints in basis and coefficient matrices; this method decomposes an input matrix into non-negative basis to solve the aforementioned issue. NMF is applied in infrared non-destructive testing (IRNDT) also through two ways of computations using gradient descend (GD) and nonnegative least square (NNLS).An ensemble joint sparse low-rank matrix decomposition is presented for detecting thermal defects in CFRP specimens by using the optical pulse thermography (OPT) diagnosis system. Semi-NMF briefly discussed for thermography without any detailed analyses. Despite considerable developments in the field of thermography, the application of semi-, convex- , and sparse- NMF remains uninvestigated. Changing the bases in NMF method to convert matrix approximation to a segmentation problem while selecting predominant basis remains challenging. This study shows an application of low-rank semi-, convex-, and sparse-NMF in thermography and breast cancer screening to detect defects and identify symptomatic patients, respectively.