ORIGINAL PAPER Singular Value Decomposition Using Jacobi Algorithm in pMRI and CS Sohaib A. Qazi 1 • Abeera Saeed 1 • Saima Nasir 1 • Hammad Omer 1 Received: 15 December 2016 / Revised: 11 March 2017 / Published online: 30 March 2017 Ó Springer-Verlag Wien 2017 Abstract Parallel magnetic resonance imaging (pMRI) and compressed sensing (CS) have been recently used to accelerate data acquisition process in MRI. Matrix inversion (for rectangular matrices) is required to reconstruct images from the acquired under-sampled data in various pMRI algorithms (e.g., SENSE, GRAPPA) and CS. Singular value decomposition (SVD) provides a mechanism to accurately estimate pseudo-inverse of a rectangular matrix. This work proposes the use of Jacobi SVD algorithm to reconstruct MR images from the acquired under-sampled data both in pMRI and in CS. The use of Jacobi SVD algorithm is proposed in advance MRI reconstruction algorithms, including SENSE, GRAPPA, and low-rank matrix estimation in L ? S model for matrix inversion and estimation of singular values. Experiments are performed on 1.5T human head MRI data and 3T cardiac perfusion MRI data for different acceleration factors. The reconstructed images are analyzed using artifact power and central line profiles. The results show that the Jacobi SVD algorithm successfully reconstructs the images in SENSE, GRAPPA, and L ? S algorithms. The benefit of using Jacobi SVD algorithm for MRI image reconstruction is its suitability for parallel computation on GPUs, which may be a great help in reducing the image reconstruction time. 1 Introduction Magnetic resonance imaging (MRI) is a non-invasive medical imaging modality that produces two- or three-dimensional detailed anatomical images of human body without the use of harmful radiations [1]. In the conventional MRI scan, k-space is & Sohaib A. Qazi sohaibqazimm@gmail.com 1 Department of Electrical Engineering, COMSATS Institute of Information Technology, Islamabad, Pakistan 123 Appl Magn Reson (2017) 48:461–471 DOI 10.1007/s00723-017-0874-0 Applied Magnetic Resonance