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              <p>Let A in R^{m x n} be an arbitrary, known matrix and e a q-sparse adversarial vector. Given y = A x* + e and q, we seek the smallest set containing x*—hence the one conveying maximal information about x*—that is uniformly recoverable from y without knowing e. While exact recovery of x* via strong (and often impractical) structural assumptions on A or x* (e.g., restricted isometry, sparsity) is well studied, recoverability for arbitrary A and x* remains open. Our main result shows that the best that one can hope to recover is x* + ker(U), where U is the unique projection matrix onto the intersection of rowspaces of all possible submatrices of A obtained by deleting 2q rows. Moreover, we prove that every x that minimizes the l_0-norm of y - A x lies in x* + ker(U), which then gives a constructive approach to recover this set.</p>
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            <ref type="url">http://www.iisc.ernet.in/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>