Optimization algorithms in compressive sensing (CS) sparse magnetic resonance imaging (MRI)

Magnetic Resonance Imaging (MRI) is an essential instrument in clinical diagnosis; however, it is burdened by a slow data acquisition process due to physical limitations. Compressive Sensing (CS) is a recently developed mathematical framework that offers significant benefits in MRI image speed by reducing the amount of acquired data without degrading the image quality. The process of image reconstruction involves solving a nonlinear constrained optimization problem. The reduction of reconstruction time in MRI is of significant benefit. We reformulate sparse MRI reconstruction as a Second Order Cone Program (SOCP).We also explore two alternative techniques to solving the SOCP problem directly: NESTA and specifically designed SOCP-LB.