- A fast TVL1-L2 minimization algorithm for signal reconstruction from partial Fourier data Junfeng Yang (jfyang2992gmail.com) Yin Zhang (yin.zhangrice.edu) Wotao Yin (wotao.yinrice.edu) Abstract: Recent compressive sensing results show that it is possible to accurately reconstruct certain compressible signals from relatively few linear measurements via solving nonsmooth convex ptimization 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. Keywords: compressive sensing, compressed sensing, MRI, MRI reconstruction, fast Fourier transform, discrete cosine transform Category 1: Convex and Nonsmooth Optimization Citation: TR08-27 Download: [PDF]Entry Submitted: 03/12/2009Entry Accepted: 03/13/2009Entry Last Modified: 03/30/2009Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.