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      Multiple 3-D Feature Fusion Framework for Hyperspectral Image Classification

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          Decoding by Linear Programming

          This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector \(f \in \R^n\) from corrupted measurements \(y = A f + e\). Here, \(A\) is an \(m\) by \(n\) (coding) matrix and \(e\) is an arbitrary and unknown vector of errors. Is it possible to recover \(f\) exactly from the data \(y\)? We prove that under suitable conditions on the coding matrix \(A\), the input \(f\) is the unique solution to the \(\ell_1\)-minimization problem (\(\|x\|_{\ell_1} := \sum_i |x_i|\)) \[ \min_{g \in \R^n} \| y - Ag \|_{\ell_1} \] provided that the support of the vector of errors is not too large, \(\|e\|_{\ell_0} := |\{i : e_i \neq 0\}| \le \rho \cdot m\) for some \(\rho > 0\). In short, \(f\) can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; \(f\) is recovered exactly even in situations where a significant fraction of the output is corrupted.
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            Atomic Decomposition by Basis Pursuit

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              A survey of image classification methods and techniques for improving classification performance

              D Lu, Q. Weng (2007)
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                Author and article information

                Journal
                IEEE Transactions on Geoscience and Remote Sensing
                IEEE Trans. Geosci. Remote Sensing
                Institute of Electrical and Electronics Engineers (IEEE)
                0196-2892
                1558-0644
                April 2018
                April 2018
                : 56
                : 4
                : 1873-1886
                Article
                10.1109/TGRS.2017.2769113
                2ccf560d-c862-47a0-a5a4-a3620d050c16
                © 2018
                History

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