A reconstructed image is rendered of a patient by a processor from a set of undersampled MRI data by first subtracting two repetitions of the acquired data in k-space to create a third dataset. The processor reconstructs the image by minimizing an objective function under a constraint related to the third dataset, wherein the objective function includes applying a Karhunen-Loeve Transform (KLT) to a temporal dimension of data. The objective function under the constraint is expressed as arg minf{∥φ(f)∥1 subject to ∥Af−y∥2≦ε}. The reconstructed image is an angiogram which may be a 4D angiogram. The angiogram is used to diagnose a vascular disease.