The robust recoverable information about x* from y under q-sparse adversarial e is the coset x* + ker(U) for U the projection onto the common rowspace of all A submatrices with 2q rows deleted; all minimizers of ||y - A x||_0 lie in this set, with a sharp exact-vs-trivial phase transition for i.i.d.
We begin by defining the notion of the ambiguity set, which captures all differences of signal pairs that can be explained byq-sparse corruptions
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What Can Be Recovered Under Sparse Adversarial Corruption? Assumption-Free Theory for Linear Measurements
The robust recoverable information about x* from y under q-sparse adversarial e is the coset x* + ker(U) for U the projection onto the common rowspace of all A submatrices with 2q rows deleted; all minimizers of ||y - A x||_0 lie in this set, with a sharp exact-vs-trivial phase transition for i.i.d.