title: Fast single image super-resolution using estimated low-frequency k-space data in MRI.
abstract: Single image super-resolution (SR) is highly desired in many fields but obtaining it is often technically limited in practice. The purpose of this study was to propose a simple, rapid and robust single image SR method in magnetic resonance (MR) imaging (MRI).
  
  
  
  The idea is based on the mathematical formulation of the intrinsic link in k-space between a given (modulus) low-resolution (LR) image and the desired SR image. The method consists of two steps: 1) estimating the low-frequency k-space data of the desired SR image from a single LR image; 2) reconstructing the SR image using the estimated low-frequency and zero-filled high-frequency k-space data. The method was evaluated on digital phantom images, physical phantom MR images and real brain MR images, and compared with existing SR methods.
  
  
  
  The proposed SR method exhibited a good robustness by reaching a clearly higher PSNR (25.77dB) and SSIM (0.991) averaged over different noise levels in comparison with existing edge-guided nonlinear interpolation (EGNI) (PSNR=23.78dB, SSIM=0.983), zero-filling (ZF) (PSNR=24.09dB, SSIM=0.985) and total variation (TV) (PSNR=24.54dB, SSIM=0.987) methods while presenting the same order of computation time as the ZF method but being much faster than the EGNI or TV method. The average PSNR or SSIM over different slice images of the proposed method (PSNR=26.33 dB or SSIM=0.955) was also higher than the EGNI (PSNR=25.07dB or SSIM=0.952), ZF (PSNR=24.97dB or SSIM=0.950) and TV (PSNR=25.70dB or SSIM=0.953) methods, demonstrating its good robustness to variation in anatomical structure of the images. Meanwhile, the proposed method always produced less ringing artifacts than the ZF method, gave a clearer image than the EGNI method, and did not exhibit any blocking effect presented in the TV method. In addition, the proposed method yielded the highest spatial consistency in the inter-slice dimension among the four methods.
  
  
  
  This study proposed a fast, robust and efficient single image SR method with high spatial consistency in the inter-slice dimension for clinical MR images by estimating the low-frequency k-space data of the desired SR image from a single spatial modulus LR image.
authors.affiliation: School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 200240, China.
authors.forename: Jianhua
authors.initials: J
authors.lastname: Luo
authors.affiliation: China National Aeronautical Radio Electronics Research Institute, Shanghai 200233, China.
authors.forename: Zhiying
authors.initials: Z
authors.lastname: Mou
authors.affiliation: School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. Electronic address: bjqin@sjtu.edu.cn.
authors.forename: Binjie
authors.initials: B
authors.lastname: Qin
authors.affiliation: School of Computer Science and Software Engineering, University of Wollongong, NSW 2522, Australia.
authors.forename: Wanqing
authors.initials: W
authors.lastname: Li
authors.affiliation: School of Computer and Information Technology, Beijing Jiao Tong University, China.
authors.forename: Feng
authors.initials: F
authors.lastname: Yang
authors.affiliation: University of Lyon; CNRS UMR 5220; Inserm U1206; INSA Lyon, Creatis, France.
authors.forename: Marc
authors.initials: M
authors.lastname: Robini
authors.affiliation: University of Lyon; CNRS UMR 5220; Inserm U1206; INSA Lyon, Creatis, France.
authors.forename: Yuemin
authors.initials: Y
authors.lastname: Zhu
mesh_terms: D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging; D019047:Phantoms, Imaging / Q000592:standards
keywords: Image interpolation; Magnetic resonance imaging; Super-resolution; k-Space data