dc.contributor.author Yang, JunfengZhang, YinYin, Wotao 2018-06-19T17:13:03Z 2018-06-19T17:13:03Z 2008-10 Yang, Junfeng, Zhang, Yin and Yin, Wotao. "A Fast TVL1-L2 Minimization Algorithm for Signal Reconstruction from Partial Fourier Data." (2008) https://hdl.handle.net/1911/102105. https://hdl.handle.net/1911/102105 Recent compressive sensing results show that it is possible to accurately reconstruct certain compressible signals from relatively few linear measurements via solving nonsmooth convex optimization problems. In this paper, we propose a simple and fast algorithm for signal reconstruction from partial Fourier data. The algorithm minimizes the sum of three terms corresponding to total variation, $\ell_1$-norm regularization and least squares data fitting. It uses an alternating minimization scheme in which the main computation involves shrinkage and fast Fourier transforms (FFTs), or alternatively discrete cosine transforms (DCTs) when available data are in the DCT domain. We analyze the convergence properties of this algorithm, and compare its numerical performance with two recently proposed algorithms. Our numerical simulations on recovering magnetic resonance images (MRI) indicate that the proposed algorithm is highly efficient, stable and robust. 10 pp A Fast TVL1-L2 Minimization Algorithm for Signal Reconstruction from Partial Fourier Data Technical report October 2008 Text
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