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Compressed sensing (CS) exploits the sparsity of MR images to enable accurate reconstruction from undersampled k-space data. Recent CS methods have employed analytical sparsifying transforms such as wavelets and finite differences. In this paper, we propose a novel framework for adaptively learning the sparsifying transform (dictionary), and reconstructing the image simultaneously from highly undersampled k-space data. The sparsity is enforced on overlapping image patches. The proposed alternating reconstruction algorithm learns the sparsifying dictionary, and uses it to remove aliasing and noise in one step, and subsequently restores and fills-in the k-space data in the other step. Experimental results demonstrate dramatic improvements in reconstruction error using the proposed adaptive dictionary as compared to previous CS methods.