Reconstruction of Undersampled Cardiac Cine MRI data Using Compressive Sensing Principles

Reduction of MRI data acquisition time is an important goal in the MRI field. Undersampling k-t space is a solution to reduce acquisition time. MR images may have sparse or compressible presentations in appropriate transform domains, such as wavelets. According to the Compressive Sensing (CS) theory, they can be recovered from randomly undersampled k-t space data that guarantees incoherency between sparsifying transform and sampling operator. However, pure random k-space sampling can be more time-consuming than full k-space sampling because of MRI principles. In this paper, we propose a new method based on hidden Markov models (HMM) to undersample k-space along the phase-encoding direction. To this end, we cluster extracted features of each k-space line by fuzzy c-means (FCM) method and consider the resulting class labels as the states of a Markov chain. Then we train a HMM and find the related transition matrix to each k-space line. We choose the lines having more non-diagonal transition matrices to sample data along them. We reconstruct the image by minimizing the L1 norm subject to data consistency using conjugate-gradient method and use simulation to set the parameters of the proposed method (e.g., iteration number). We apply our method to reconstruct undersampled Cardiac Cine MRI data with and without sparsifying transform, successfully. The use of fuzzy clustering as an intermediate tool to study complicated phenomena by HMM, applicability to non-dynamic MRI data and simplicity can be accounted as the specifications of the proposed method.