Optimization algorithms in compressive sensing (CS) sparse magnetic resonance imaging (MRI)
Date
2010-06-01
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Abstract
Magnetic Resonance Imaging (MRI) is an essential instrument in clinical diag-
nosis; however, it is burdened by a slow data acquisition process due to physical
limitations. Compressive Sensing (CS) is a recently developed mathematical
framework that o ers signi cant bene ts 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 signi cant bene t.
We reformulate sparse MRI reconstruction as a Second Order Cone Program
(SOCP).We also explore two alternative techniques to solving the SOCP prob-
lem directly: NESTA and speci cally designed SOCP-LB.
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Keywords
Compressive sensing, Sparse MRI, Convex optimization