Comparing measures of sparsity
IEEE Transactions on Information Theory
On the total variation dictionary model
IEEE Transactions on Image Processing
Conditions for a unique non-negative solution to an underdetermined system
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
On the impact of routing matrix inconsistencies on statistical path monitoring in overlay networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Label propagation algorithm based on non-negative sparse representation
LSMS/ICSEE'10 Proceedings of the 2010 international conference on Life system modeling and simulation and intelligent computing, and 2010 international conference on Intelligent computing for sustainable energy and environment: Part III
Sparse nonnegative matrix factorization with ℓ0-constraints
Neurocomputing
High-resolution ranging method based on low-rate parallel random sampling
Digital Signal Processing
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
ACM Transactions on Graphics (TOG)
Theoretical Computer Science
Recovering non-negative and combined sparse representations
Digital Signal Processing
Non-negative sparse decomposition based on constrained smoothed ℓ0 norm
Signal Processing
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An underdetermined linear system of equations Ax = b with nonnegativity constraint x ges 0 is considered. It is shown that for matrices A with a row-span intersecting the positive orthant, if this problem admits a sufficiently sparse solution, it is necessarily unique. The bound on the required sparsity depends on a coherence property of the matrix A. This coherence measure can be improved by applying a conditioning stage on A, thereby strengthening the claimed result. The obtained uniqueness theorem relies on an extended theoretical analysis of the lscr0 - lscr1 equivalence developed here as well, considering a matrix A with arbitrary column norms, and an arbitrary monotone element-wise concave penalty replacing the lscr1-norm objective function. Finally, from a numerical point of view, a greedy algorithm-a variant of the matching pursuit-is presented, such that it is guaranteed to find this sparse solution. It is further shown how this algorithm can benefit from well-designed conditioning of A .