Compressed sensing MRI (CS-MRI) aims to significantly reduce the measurements required for image reconstruction in order to accelerate the overall imaging speed. The sparsity of the MR images in transformation bases is one of the fundamental criteria for CS-MRI performance. Sparser representations can require fewer samples necessary for a successful reconstruction or achieve better reconstruction quality with a given number of samples. Generally, there are two kinds of 'sparsifying' transforms: predefined transforms and data-adaptive transforms. The predefined transforms, such as the discrete cosine transform, discrete wavelet transform and identity transform have usually been used to provide sufficiently sparse representations for limited types of MR images, in view of their isolation to the object images. In this paper, we present singular value decomposition (SVD) as the data-adaptive 'sparsity' basis, which can sparsify a broader range of MR images and perform effective image reconstruction. The performance of this method was evaluated for MR images with varying content (for example, brain images, angiograms, etc), in terms of image quality, reconstruction time, sparsity and data fidelity. Comparison with other commonly used sparsifying transforms shows that the proposed method can significantly accelerate the reconstruction process and still achieve better image quality, providing a simple and effective alternative solution in the CS-MRI framework.