De-mixing problems in spectroscopic imaging often require finding sparse non-negative linear combinations of library functions to match observed data. Due to misalignment and uncertainty in data measurement, the known library functions may not represent the data as well as their proper deformations. To improve data adaptivity, we expand the library to one with a group structure and impose a structured sparsity constraint so that the coefficients for each group should be sparse or even 1-sparse. Since the expanded library is a highly coherent (redundant) dictionary, it is difficult to obtain good solutions using convex methods such as non-negative least squares (NNLS) or L1 norm minimization. We study efficient non-convex penalties such as the ratio/difference of L1 and L2 norms, as sparsity penalties to be added to the objective in NNLS-type models. We show an exact recovery theory of the sparsest solution by minimizing the ratio/difference norms under a uniformity condition. For solving the related unconstrained non-convex models, we develop a scaled gradient projection algorithm that requires solving a sequence of strongly convex quadratic programs.