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A Simple Proof for Recoverability of L1-Minimization (II): the Nonnegativity Case
When using L1 minimization to recover a sparse, nonnegative solution to a under-determined linear system of equations, what is the highest sparsity level at which recovery can still be guaranteed? Recently, Donoho and ...
Accelerating the Lee-Seung Algorithm for Nonnegative Matrix Factorization
Approximate nonnegative matrix factorization is an emerging technique with a wide spectrum of potential applications in data analysis. Currently, the most-used algorithms for this problem are those proposed by Lee and ...
Solution-Recovery in L1-norm for Non-square Linear Systems: Deterministic Conditions and Open Questions
Consider an over-determined linear system A'x = b and an under-determined linear system By = c. Given b = A'x* + h, under what conditions x* will minimize the residual A'x - b in L1-norm? On the other hand, given c = Bh, ...
A Simple Proof for Recoverability of L1-Minimization: Go Over or Under?
It is well-known by now that L1 minimization can help recover sparse solutions to under-determined linear equations or sparsely corrupted solutions to over-determined equations, and the two problems are equivalent under ...