engleski

Fast LCNN ica for Unsupervised Hyperspectral Image Classifier

Since in remote sensing each pixel could have its own unique radiation source including man-made objects associated with different spectral reflectance matrix A, we could not average over neighborhood pixels. Instead, we solve pixel-by-pixel independent classes analysis (ica) without pixel average by Lagrange Constraint of the data measurement model and Gibbs&#8217 ; equal a priori probability assumption based on Shannon&#8217 ; s Entropy with probability normalization condition for an arbitrary number of M classes that is bounded by the spectral data components N. We formulate the Fast Lagrangian method to maximize the Shannon entropy with the equality constraints in order to achieve O(N) numerical complexity contrary to the O(N2) numerical complexity associated with the solution of the inverse problem required in the classical Lagrangian formulation. Trivial equal probability solution with uniformly distributed class vector is avoided by introducing additional set of the inequality constraints. The unknown spectral reflectance matrix A is estimated blindly in non-parameterized form minimizing an LMS energy function . We apply the Riemannian metric to the gradient learning for reproducing the biological Hebbian rule in terms of a full rank vector outer product formula and demonstrate faster convergence than standard Euclidean gradient. Since the proposed Fast Lagrangian method has O(N) numerical complexity we have achieved a real time hyperspectral remote sensing capability as platform moves, samples and processes. A FPGA firmware implementation for massive pixel parallel algorithm has been fired for patent.

Hyper-spectral imaging; sub-pixel resolution; constrained maximum entropy; fast Lagrangian method; unsupervised neural networks; independent component analysis; independent class analysis.

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