Fast Non-Convex Statistical Compressed Sensing MRI Reconstruction Based on Approximated Lp(0

Il Yong Chun¹, Thomas Talavage¹, ²

¹School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, United States; ²Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, United States

we propose a fast constrained L(p,)-L2-norm (L(p,) is an approximated Lp-qusi-norm) minimization algorithm, based on 1) p- and -dependent weighting techniques, and 2) an efficient split Bregman-based (known to have rapid convergence, especially with an L1-norm ) reweighted L1-minimization algorithm. This L(p,)-L2-norm minimization achieves exact reconstruction from fewer measurements than are required for the L1-L2-norm case.

Keywords

ability accomplish accuracy achievable achieves allow analytically applications applied approximated approximation become behavior benefit biomedical circulant collection combinatorial comparable completed compressed computations computed computer constrained continue convergence convex coverage criteria dependent depends directly discrete efficient efficiently effort electrical element engineering enormous equivalent error escape escaping especially exact expected fast fewer finally formulated full function generated global graphically guarantee hard help hong identical impossible inner instead introduced introducing invert iteration iterations known linear local longer loop make many matrix measured medicine minimization noise norm note often optimization orthogonal outer partial perfect perturbed phantom practical prob problem property propose proposed providing quality radial rapid reasonable reconstruct reconstructed reconstruction reducing reduction remarkable representation represents required requires restricted robustly samples satisfies school sensing series solution solutions solve solved solving space sparse split statistical stopping strong structure subject sufficient table termination tractable trans transform transforms update updated updates variance want wavelet weaker west wise written zero