Reconstruction of reflectance spectra using robust nonnegative matrix factorization

Abstract

Abstract-In this correspondence, we present a robust statistics-based nonnegative matrix factorization (RNMF) approach to recover the measurements in reflectance spectroscopy. The proposed algorithm is based on the minimization of a robust cost function and yields two equations updated alternatively. Unlike other linear representations, such as principal component analysis, the RNMF technique is resistant to outliers and generates nonnegative-basis functions, which balance the logical attractiveness of measurement functions against their physical feasibility. Experimental results on a spectral library of reflectance spectra are presented to illustrate the much improved performance of the RNMF approach.

Algorithms and applications for approximate nonnegative matrix factorization

“…(Guillamet et al, 2001) have suggested the use of a diagonal weight matrix Q in a new factorization model, AQ ≈ WHQ, in an attempt to compensate for feature redundancy in the columns of W. This problem can also be alleviated using column stochastic constraints on H . Other approaches that propose alternative cost function formulations include but are not limited to (Hamza and Brady, 2006;Dhillon and Sra, 2005). A theoretical analysis of nonnegative matrix factorization of symmetric matrices can be found in (Catral et al, 2004).…”

Robust Nonnegative Matrix Factorization via Half-Quadratic Minimization

“…(8) reduces to the weighted NMF presented in Eq. (12). A local minimum can be found by the following update rules…”

“…Recently, some variants have been proposed to improve the robustness of original NMF. The L 1 −L 2 function in [12] was used for the purpose of robust factorization. The optimization problem is solved by a general gradient descent scheme, which is computational expensive.…”

Regularized nonnegative matrix factorization: Geometrical interpretation and application to spectral unmixing

“…Hence, it has already found diverse applications in data spectral analysis, mostly as a tool for blind unmixing or extraction of pure spectra (endmembers) from observed noisy mixtures. Examples include Raman scattering (e.g., Sajda et al, 2003;Li et al, 2007;Miron et al, 2011), hyperspectra unmixing (e.g., Miao and Qi, 2007;Zymnis et al, 2007;Zhang et al, 2008;Jia and Qian, 2009;Guo et al, 2009;Huck et al, 2010;Chan et al, 2011;Heylen et al, 2011;Qian et al, 2011;Iordache et al, 2011;2012;Plaza et al, 2012;Bioucas-Dias et al, 2012;Zdunek, 2012), spectral unmixing in microscopy (e.g., Pengo et al, 2010), chemical shift imaging (e.g., Sajda et al, 2004), reflectance spectroscopy (e.g., Pauca et al, 2006;Hamza and Brady, 2006), fluorescence spectroscopy (e.g., Gobinet et al, 2004), two-photon spectroscopic analysis (e.g., Hancewicz and Wang, 2005), astrophysical ice spectra unmixing (e.g., Igual et al, 2006;Igual and Llinares, 2008;Llinares et al, 2010), and gas chromatography-mass spectrometry (e.g., Likic, 2009). …”