Unique solvability of under-determined sparse blind separation of nonnegative and overlapped data
Conference
Sun, Y, Xin, J. (2010). Unique solvability of under-determined sparse blind separation of nonnegative and overlapped data
. 70-77. 10.2316/p.2010.710-017
Sun, Y, Xin, J. (2010). Unique solvability of under-determined sparse blind separation of nonnegative and overlapped data
. 70-77. 10.2316/p.2010.710-017
We study the unique solvability of sparse blind separation of n non-negative sources from m linear mixtures in the under-determined regimem < n. Such source signals arise in nuclear magnetic resonance data. The geometric properties of themixturematrix and sparseness structure of source matrix are closely related to the unique identification of the mixing matrix. We illustrate and establish necessary and sufficient conditions for the unique separation up to scaling and permutation. We also present a novel algorithm based on data geometry, source sparseness, and l1 minimization. Numerical results substantiate the uniqueness of the source signal recovery, and show satisfactory performance of our algorithm on chemical data.
