Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this paper, we propose to revisit the NMF as a multi-objective problem, in particular a bi-objective one, where the objective functions defined in both input and feature spaces are taken into account. By taking the advantage of the sum-weighted method from the literature of multi-objective optimization, the proposed bi-objective NMF determines a set of nondominated, Pareto optimal, solutions instead of a single optimal decomposition. Moreover, the corresponding Pareto front is studied and approximated. Experimental results on unmixing real hyperspectral images confirm the efficiency of the proposed bi-objective NMF compared with the state-of-the-art methods

Nonlinear Hyperspectral Unmixing With Robust Nonnegative Matrix Factorization

International audienceWe introduce a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. The new model extends the commonly used linear mixing model by introducing an additional term accounting for possible nonlinear effects, that are treated as sparsely distributed additive outliers.With the standard nonnegativity and sum-to-one constraints inherent to spectral unmixing, our model leads to a new form of robust nonnegative matrix factorization with a group-sparse outlier term. The factorization is posed as an optimization problem which is addressed with a block-coordinate descent algorithm involving majorization-minimization updates. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods

A spectral dissimilarity constrained nonnegative matrix factorization based cancer screening algorithm from hyperspectral fluorescence images

Bioluminescence from living body can help screen cancers without penetrating the inside of living body. Hyperspectral imaging technique is a novel way to obtain physical meaningful signatures, providing very fine spectral resolution, that can be very used in distinguishing different kinds of materials, and have been widely used in remote sensing field. Fluorescence imaging has proved effective in monitoring probable cancer cells. Recent work has made great progress on the hyperspectral fluorescence imaging techniques, which makes the elaborate spectral observation of cancer areas possible. So how to propose the proper hyperspectral image processing methods to handle the hyperspectral medical images is of practical importance. Cancer cells would be distinguishable with normal ones when the living body is injected with fluorescence, which helps organs inside the living body emit lights, and then the signals can be catched by the passive imaging sensor. Spectral unmixing technique in hyperspectral remote sensing has been introduced to detect the probable cancer areas. However, since the cancer areas are small and the normal areas and the cancer ares may not pure pixels so that the predefined endmembers would not available. In this case, the classic blind signals separation methods are applicable. Considering the spectral dissimilarity between cancer and normal cells, a novel spectral dissimilarity constrained based NMF method is proposed in this paper for cancer screening from fluorescence hyperspectral images. Experiments evaluate the performance of variable NMF based method and our proposed spectral dissimilarity based NMF methods: 1) The NMF methods do perform well in detect the cancer areas inside the living body; 2) The spectral dissimilarity constrained NMF present more accurate cancer areas; 3) The spectral dissimilarity constraint presents better performance in different SNR and different purities of the mixing endmembers. © 2012 IEEE

Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing

In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully-constrained unmixing, with both the non-negativity and sum-to-one constraints, while the second one deals with the non-negativity and the sparsity-promoting of the abundances. The corresponding optimization problems are solved efficiently using an alternating direction method of multipliers (ADMM) approach. Experiments on synthetic and real hyperspectral images validate the performance of the proposed algorithms for different scenarios, demonstrating that the correntropy-based unmixing is robust to outlier bands.Comment: 23 page

NON-MATRIX FACTORIZATION FOR BLIND IMAGE SEPARATION

Hyperspectral unmixing is a process to identify the constituent materials and estimate the corresponding fractions from the mixture, nonnegative matrix factions ( NMF ) is suitable as a candidate for the linear spectral mixture mode, has been applied to the unmixing hyperspectral data. Unfortunately, the local minima is cause by the nonconvexity of the objective function  makes the solution nonunique, thus only the nonnegativity constraint is not sufficient enough to lead to a well define problems. Therefore, two inherent characteristic of hyperspectal data, piecewise smoothness ( both temporal and spatial ) of spectral data and sparseness of abundance fraction of every material, are introduce to the NMF. The adaptive potential function from discontinuity adaptive Markov random field model is used to describe the smoothness constraint while preserving discontinuities is spectral data.  At the same time two NMF algorithms, non smooth NMS and NMF with sparseness constraint, are used to quantify the degree of sparseness of material abundances. Experiment using the synthetic and real data demonstrate the proposed algorithms provides an effective unsupervised technique for hyperspectial unmixing