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Coronary magnetic resonance imaging (MRI) is a noninvasive imaging modality for diagnosis of coronary artery disease. One of the limitations of coronary MRI is its long acquisition time due to the need of imaging with high spatial resolution and constraints on respiratory and cardiac motions. Compressed sensing (CS) has been recently utilized to accelerate image acquisition in MRI. In this paper, we develop an improved CS reconstruction method, Bayesian least squares-Gaussian scale mixture (BLS-GSM), that uses dependencies of wavelet domain coefficients to reduce the observed blurring and reconstruction artifacts in coronary MRI using traditional l1 regularization. Images of left and right coronary MRI was acquired in 7 healthy subjects with fully-sampled k-space data. The data was retrospectively undersampled using acceleration rates of 2, 4, 6, and 8 and reconstructed using l1 thresholding, l1 minimization and BLS-GSM thresholding. Reconstructed right and left coronary images were compared with fully-sampled reconstructions in vessel sharpness and subjective image quality (1-4 for poor-excellent). Mean square error (MSE) was also calculated for each reconstruction. There were no significant differences between the fully sampled image score versus rate 2, 4, or 6 for BLS-GSM for both right and left coronaries (=N.S.). However, for l1 thresholding significant differences (p <; 0.05) were observed for rates higher than 2 and 4 for right and left coronaries respectively. l1 minimization also yields images with lower scores compared to the reference for rates higher than 4 for both coronaries. These results were consistent with the quantitative vessel sharpness readings. BLS-GSM allows acceleration of coronary MRI with acceleration rates beyond what can be achieved with l1 regularization.