Constrained magnetic resonance image reconstruction from incomplete frequency measurements - Deng, Jun (2015)
In this thesis, we develop constrained reconstructions methods to reconstruct high quality MR images from down-sampled k-space data by exploiting sparsity of MR images under the theory of Compressed Sensing. In the first work, we present an orthonormal-expansion L1 optimization technique to improve computational efficiency of existing methods without sacrificing the reconstruction accuracy. In order to achieve more accurate reconstructions especially in high under-sampling ratios, a novel method for motion-compensated reference-driven MR image reconstruction is presented in the second work with two sources of constraints: sparsity and prior information from a reference image. In the third work, we focus on reconstructions of MR images that have metallic implants. In order to reduce scan time incurred to fully correct metal artefacts and meanwhile improve SNR of results brought by the state-of-the-art methods, we propose a projection on convex set reconstruction technique to combine CS denoising and parallel MRI.