ENBIS-18 in Nancy

2 – 25 September 2018; Ecoles des Mines, Nancy (France) Abstract submission: 20 December 2017 – 4 June 2018

Online NMF with Minimum Volume Constraint for Hyperspectral Pushbroom Imaging Systems and the Estimation of the Regularization Parameter

3 September 2018, 14:00 – 14:20


Submitted by
Ludivine NUS
Ludivine Nus (CRAN), Sebastian Miron (CRAN), David Brie (CRAN)
This work aims at developing real-time hyperspectral image unmixing methods. These methods are required in industrial applications for controlling and sorting input materials. One of the most employed technical solutions makes use of a pushbroom imager; the hyperspectral data cube is acquired slice by slice, sequentially in time, by moving the objects directly on the conveyor belt.

A relevant method dedicated to this type of applications is on-line Non-negative Matrix Factorization (NMF), which is an adaptive version of the classical NMF. For a non-negative matrix X, the NMF consists in finding two non-negative matrices S and A such that: X~SA. The goal of on-line NMF methods is to sequentially update in real-time the endmembers (S) and the abundances (A) for each new acquired sample. In general, the NMF suffers from non-uniqueness of the solution. In order to reduce the set of admissible solutions, we integrate a minimum volume simplex (MVS) constraint, resulting in the on-line MVS-NMF method.

However, the effectiveness of the online MVS-NMF is hampered by the optimal determination of the strength of minimum volume simplex term. To answer this problem, we formulate it as a bi-objective optimization problem, resulting in a linear plot (response curve) of the data fitting versus regularization cost. In order to estimate the optimal value of the MVS hyperparameter, we propose to use the Minimum Distance Criterion (MDC); This choice of MDC is motivated by the fact that the MDC solution is unique under mild conditions, unlike other criteria (e.g., the maximum curvature of L-curve). By performing experiments on a simulated image and on real hyperspectral wood data, we show that our method is well-suited for the estimation of the optimal value of the MVS hyperparameter.

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