In this paper we propose a new method for estimating the mixing matrix, A, in the linear model X = AS, for the problem of underdetermined Sparse Component Analysis (SCA). Contrary to most existing algorithms, in the proposed algorithm there may be more than one active source at each instant (i.e. in each column of the source matrix S), and the number of sources is not required to be known in advance. Since in the cases where more than one source is active at each instant, data samples concentrate around multidimensional subspaces, the idea of our method is to first estimate these subspaces and then estimate the mixing matrix from these estimated subspaces.