title: Highly undersampled magnetic resonance image reconstruction via homotopic l(0) -minimization.
abstract: In clinical magnetic resonance imaging (MRI), any reduction in scan time offers a number of potential benefits ranging from high-temporal-rate observation of physiological processes to improvements in patient comfort. Following recent developments in compressive sensing (CS) theory, several authors have demonstrated that certain classes of MR images which possess sparse representations in some transform domain can be accurately reconstructed from very highly undersampled K-space data by solving a convex l(1) -minimization problem. Although l(1)-based techniques are extremely powerful, they inherently require a degree of over-sampling above the theoretical minimum sampling rate to guarantee that exact reconstruction can be achieved. In this paper, we propose a generalization of the CS paradigm based on homotopic approximation of the l(0) quasi-norm and show how MR image reconstruction can be pushed even further below the Nyquist limit and significantly closer to the theoretical bound. Following a brief review of standard CS methods and the developed theoretical extensions, several example MRI reconstructions from highly undersampled K-space data are presented.
authors.affiliation: Center for Advanced Imaging Research, Mayo Clinic College of Medicine, Rochester, MN 55905 USA. trzasko.joshua@mayo.edu
authors.forename: Joshua
authors.initials: J
authors.lastname: Trzasko
authors.forename: Armando
authors.initials: A
authors.lastname: Manduca
mesh_terms: D000818:Animals; D016477:Artifacts; D001185:Artificial Intelligence; D044962:Data Compression / Q000379:methods*; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods; D008279:Magnetic Resonance Imaging / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods; D018401:Sample Size; D013131:Spine / Q000033:anatomy & histology; D013382:Subtraction Technique; D014953:Wrist / Q000033:anatomy & histology