@CONFERENCE\{IMM2011-06004,
    author       = "L. G\'{o}mez-Chova and A. A. Nielsen and G. Camps-Valls",
    title        = "Explicit signal to noise ratio in reproducing kernel Hilbert spaces",
    year         = "2011",
    month        = "jul",
    pages        = "3570-3573",
    booktitle    = "{IEEE} {IGARSS}",
    volume       = "",
    series       = "",
    editor       = "",
    publisher    = "",
    organization = "",
    address      = "Vancouver, Canada",
    note         = "invited contribution",
    url          = "http://www.imm.dtu.dk/pubdb/p.php?6004",
    abstract     = "This paper introduces a nonlinear feature extractionmethod based on kernels for remote sensing data analysis. The proposed approach is based on theMinimum Noise Fraction (MNF) transform, which extends principal component analysis (PCA) by maximizing the signal variance while also minimizing the estimated noise variance. The kernel {MNF} (KMNF) is the standard kernelization of the canonical {MNF} in which noise is estimated in the original input space and then both signal and noise are transformed via suitable mappings endorsed with the reproducing kernel property. We here propose an alternative {KMNF} in which the noise is explicitly estimated in the reproducing kernel Hilbert space. This simplifies the formulation and method’s application, and enables {KMNF} dealing with non-linear relations among the noise and the signal. Results show that the proposed {KMNF} method provides the most noise-free features when confronted with standard {PCA,} {MNF} and the previous version of {KMNF}. Extracted features with the explicit {KMNF} also improve hyperspectral image classification."
}