TGV For Undersampled MRI Reconstruction

Magnetic Resonance Imaging (MRI) is a relatively new, non-invasiveimaging modality. In modern clinical therapy, MRI is becoming more andmore popular due to its excellent representation of soft tissues,multi-imaging parameters, high resolution, arbitrary slice imaging andinherent absence of emitted ionizing radiation [1][2].Contemporary MRI applications require high spatial, temporalresolution, good signal-to-noise (SNR) and high imaging speed [3][4].However, conventional MRI applications take such a long time.Meanwhile, considering movement of the patient that makes the image blurand contrast distortion, MRI cannot be used to research movement organsand nerve system before. It is becoming more and more important to speedup imaging, improve quality of images and patient comfort.Actually, it is imaging speed to prevent development of MRIapplications. To accelerate imaging, besides improving equipmentcapability, reconstruction from partial k-space is a very common and lowcost strategy. It short imaging time without changing the hardware of MRIand the scan way.The total variation (TV) method, which is originally designed forimage denoising, generally applied in MRI reconstruction so far. Bychanging the image model to minimize total variation, this method purposesto remove the unwanted image noise and small-scale details of the sametime and protect those who are non-consecutive region mutations. Based onthe limiting assumption of piecewise constant images, it doesn't performthe feat at all time. Total generalized variation (TGV) was introduced to thereconstruction of MRI data collected in partial k-space to improve imagequality in this case. This paper compares TGV method and TV method applied in manyexperiments. And the Newton's method and conjugate gradient method isapplied to solve the TV minimization problems. The TGV method performsbetter for reconstruction from images composed of complex structure, suchas the T2brain images, while for the images with simple structure, such asthe Shepp-Logan phantom, it achieves preferable or even worse results andcost more time.