A Splitting Bregman-Based Compressed Sensing Approach for Radial UTE MRI


A splitting Bregman-based compressed-sensing (CS) approach (CS-SplitBerg), using the nonuniform fast Fourier transform, is proposed to reconstruct radial magnetic resonance (MR) images from undersampled k-space measurements. Using the splitting Bregman framework, the proposed CS-SplitBerg approach takes fully into account the measurement noise and exploits the combined sparsity of MR images, i.e., ℓ1-norm and total variation regularization. With convergence guaranteed, the CS-SplitBerg approach uses the Bregman update process and some auxiliary variables to relax the constrained optimization problem to a sequence of easily solved unconstrained minimization problems. Experimental results using both a phantom example and a mouse cardiac example demonstrate that, under different undersampling rates, the CS-SplitBerg approach performs better than the CS-CG approach, which was introduced in our previous work. With an affordable computational cost by considering the influences of noise, the CS-SplitBerg approach can further reduce the necessary number of MR imaging (MRI) measurements for the recovery and better differentiate true MRI images from noisy data.


Electrical and Computer Engineering


National Science Foundation of China
Specialized Research Fund for the Doctoral Program of High Education of China
Sichuan Province Applied Basis Research Project


This work was supported in part by the National Science Foundation of China under Grant 61371049 and Grant 60871056, by the Specialized Research Fund for the Doctoral Program of High Education of China under Grant 20120185110013, and by the Sichuan Province Applied Basis Research Project under Grant 2013JY0058.

Keywords and Phrases

Constrained optimization; Fast Fourier transforms; Image denoising; Image processing; Magnetic resonance imaging; Optimization; Signal reconstruction; Auxiliary variables; Compressive sensing; Computational costs; Constrained optimi-zation problems; Non-uniform fast Fourier transforms; Total variation regularization; Ultrashort echo time; Unconstrained minimization problem; Compressed sensing; Compressed sensing (CS); Magnetic resonance imaging (MRI); Ultrashort echo time (UTE)

International Standard Serial Number (ISSN)

1051-8223; 1558-2515

Document Type

Article - Journal

Document Version


File Type





© 2016 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jun 2016