For the first we frame collaborative filtering as a Blind Compressed Sensing (BCS) problem. Our formulation stems from the standard matrix factorization approach of decomposing the ratings matrix into a user latent factor matrix and an item latent factor matrix. Previous studies assumed both these matrices to be dense, i.e. both users and items had non-zero values for all factors. This assumption is true for the user matrix but not for the item matrix. It is not possible for an item matrix to have non zero values for all the factors, i.e. the item matrix is likely to be sparse. This assumption leads to the BCS formulation. We compared our proposed method with state-of-the-art matrix factorization approaches; we find that our method yields better accuracy compared to these.