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# Strategic Protection Against Data Injection Attacks on Power Grids

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IEEE Transactions on Smart Grid

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### Most cited references15

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### Compressed sensing

(2006)
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• Abstract: found
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Is Open Access

### Decoding by Linear Programming

(2005)
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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### Enhancing Sparsity by Reweighted ℓ 1 Minimization

(2008)
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### Author and article information

###### Journal
IEEE Transactions on Smart Grid
IEEE Trans. Smart Grid
Institute of Electrical and Electronics Engineers (IEEE)
1949-3053
1949-3061
June 2011
June 2011
: 2
: 2
: 326-333
###### Article
10.1109/TSG.2011.2119336