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"abstract": "We consider the problem of recovering an invertible $n \\times n$ matrix $A$ and a sparse $n \\times p$ random matrix $X$ based on the observation of $Y = AX$ (up to a scaling and permutation of columns of $A$ and rows of $X$). Using only elementary tools from the theory of empirical processes we show that a version of the Er-SpUD algorithm by Spielman, Wang and Wright with high probability recovers $A$ and $X$ exactly, provided that $p \\ge Cn\\log n$, which is optimal up to the constant $C$.",
"authors": [
"Radoslaw Adamczak"
],
"id": "16-047",
"issue": 177,
"pages": [
1,
18
],
"title": "A Note on the Sample Complexity of the Er-SpUD Algorithm by Spielman, Wang and Wright for Exact Recovery of Sparsely Used Dictionaries",