Dictionary Design for Compressed Sensing MRI

Introduction: The recently introduced Compressed Sensing (CS) theory promises to accelerate data acquisition in magnetic resonance imaging (MRI) [1-3]. One of the important requirements in CS MRI is that the image has a sparse representation. This sparse representation is crucial for successful recovery in CS. Generally speaking, sparser representations yield improved performance in terms of either further reduction in the number of measurements necessary for successful recovery or improved reconstruction quality for a given number of measurements. In this work, we propose a framework for designing and utilizing sparse dictionaries in CS MRI applications. Reconstruction results demonstrate that the proposed technique can yield significantly improved image quality compared to commonly used sparsity transforms in CS MRI. Theory: Let D denote a sparsity dictionary, u F the undersampled Fourier measurement matrix, and b the acquired k-space data. Under the assumption that the image has a sparse representation in dictionary D , the CS MRI can be represented by the following minimization problem: