Due to fundamental characteristics of MRI that limit scan speedup, sub-sampling techniques such as compressed sensing (CS) have been developed for rapid MRI. Current CS MRI approaches utilize sparsity of the image in the wavelet or other transform domains to speed-up acquisition. Another drawback of MRI is its poor signal-to-noise ratio (SNR), which is proportional to the image slice thickness. In this paper, we use the difference between adjacent slices as the sparse domain for CS MRI. We propose to acquire thick MRI slices and to reconstruct the thin slices from the thick slices' data, utilizing the similarity between adjacent thin slices. The acquisition of thick slices, instead of thin ones, improves the total SNR of the reconstructed image. Experimental results show that the image reconstruction quality of the proposed method outperforms existing CS MRI methods using the same number of measurements.