In this paper, the estimation of the regularization parameter of the on-line Non-negative Matrix Factorization (NMF) with minimum volume constraint on sources is addressed. Adding a volume constraint in the model is important to ensure uniqueness of the solution and good data representation. However, the effectiveness of this approach is hampered by the optimal determination of the strength of minimum volume term. To solve this problem, we formulate it as a bi-objective optimization problem and three Minimum Distance Criterion (MDC) strategies are proposed and evaluated. The three strategies yield similar results but one of them in particular yields an interesting tradeoff between accuracy and computation time.
Pushbroom imaging systems are emerging techniques for real-time acquisition of hyperspectral images. These systems are frequently used in industrial applications to control and sort products on-the-fly. In this paper, the on-line hyperspectral image blind unmixing is addressed. We propose a new on-line method based on Alternating Direction Method of Multipliers (ADMM) approach, adapted to pushbroom imaging systems. Because of the generally ill-posed nature of the unmixing problem, we impose a minimum endmembers dispersion regularization to stabilize the solution; this regularization can be interpreted as a convex relaxation of the minimum volume regularization and therefore, presents interesting optimization properties. The proposed algorithm presents faster convergence rate and lower computational complexity compared to the algorithms based on multiplicative update rules. Experimental results on synthetic and real datasets, and comparison to state-of-the-art algorithms, demonstrate the effectiveness of our method in terms of rapidity and accuracy.
This paper addresses the problem of rank tracking in real time hyperspectral image unmixing. Based on the On-line Alternating Direction Method of Multipliers (ADMM), we propose a new hyperspectral unmixing approach that integrates prior information as well as joint sparsity regularization, allowing to select only the active components on each sample of the image. This results in a semi-supervised algorithm, well adapted for on-line rank tracking for pushbroom imager. Experimental results on synthetic and real data sets demonstrate the effectiveness of our method for parameter estimation and rank change detection.
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