On the Uniqueness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations

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Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches (2012, unknown): “The uniqueness of sparse solutions to (22) when the system is underdetermined is addressed in [187].”
Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization (2012, background): “Rather recently, sparse recovery of non-negative signals in a noiseless setting (ε = 0) has been studied in [7, 19, 55, 56].”
Comparing Measures of Sparsity (2008, background): “There has also been research in the uniqueness of sparse solutions in overcomplete representations [22], [23].”
Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization (2011, background): “Thus, the L1 regularizer can be seen as a relaxation of the full additivity constraint and, in some cases, yields nonunique solutions [47].”
Collaborative Sparse Regression for Hyperspectral Unmixing (2014, background): “, η(A) ≡ max1≤k,j≤m,k =j(|ak aj |/‖ak‖2‖aj‖2)), imposes limits to the performance of sparse unmixing techniques, namely in what concerns the uniqueness of the solutions [17].”
Sparse Unmixing of Hyperspectral Data (2011, methodology): “In the previous section, we have listed a series of optimization problems aimed at computing sparse exact and approximate solutions for our hyperspectral SR problem.”