NIRS-SPM
k-t FOCUSS
Compressive MUSIC
Super-resolution Microscopy
Patch Low Rank MRI
Sparse SPM
ALOHA Inpainting
ALOHA for MRI

 k-t FOCUSS

  We developed k-t FOCUSS algorithm which is optimal from compressed sensing point of view. The basic concept of k-t FOCUSS starts from compressed sensing theory. According to compressed sensing theory, it is possible to reconstruct original signal from severely reduced sampling ratio which break Nyquist sampling limit. Therefore, this theory is getting huge interests in MRI area, because it is greatly required to reconstruct artifact free images from very sparse measurements to improve temporal resolution. There are some constraints to exploit this concept. From compressed sensing perspective, the aliasing pattern due to down sampling should incoherently appear. Therefore, the random sampling pattern is preferred. Furthermore, the original signal should be able to be sparsely transformed or compressed. And then, L1 minimization of the sparse signal is required. From these basic assumptions, we found that FOCUSS is a very suitable reconstruction algorithm. FOCUSS is originally designed to reconstruct sparse signal. Furthermore, L1 optimization is achieved by successively solving weighted L2 optimization problem, which can be easily implemented. From these advantages, we successfully developed k-t FOCUSS which reconstructs high spatio-temporal resolution of dynamic images such as a heart beating. 
Picture
Figure 1. Reconstructions from 11-fold accelerated data
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Figure 2. 2009 ISMRM workshop "Recon Challenge" winning result
 New Update
  The matlab source codes for k-t FOCUSS on Cartesian, radial, and spiral trajectories are now downloadable. ME/MC (motion estimation/motion compensation) is offered as an optional step. Please download "k-t FOCUSS.zip" and follow descriptions in the manual. Functions are provided in p-format.

 Download and File Description
  Now, Matlab source codes of k-t FOCUSS for Cartesian, radial, and spiral data are available. In order to download the source code and an example data set, registration is required. After uncompressing "k-t FOCUSS.zip", three directories named "kt_FOCUSS_Cartesian" and "kt_FOCUSS_radial" and "kt_FOCUSS_spiral" will be created which include source codes, respectively. In order to run the source code, MATLAB should be available on your system. Enclosed user guide contains file description to run the codes. 

    Download - k-t FOCUSS

If you have any problems or found any bugs, please e-mail to jong.ye@kaist.ac.kr
 References

[1] H. Jung, J. C. Ye, and E. Y. Kim, "Improved k-t BLAST and k-t SENSE using FOCUSS, Physics in Medicine and Biology, vol. 52, pp. 3201-3226, June 2007.

[2] H. Jung, K. H. Sung, K. S. Nayak, E. Y. Kim, and J. C. Ye, "k-t FOCUSS: a general compressed sensing framework for high resolution dynamic MRI, Magn Reson Med , vol. 61, pp. 103-116, January 2009.

[3] H. Jung, J. S. Park, J. H. Yoo, and J. C. Ye, "Radial k-t FOCUSS for high-resolution cardiac cine magnetic resonance imaging," Magn Reson Med, vol. 63, pp. 68-78, January 2010.

[4] J. C. Ye, S. H. Tak, Y. J. Han, and H. W. Park, "Projection Reconstruction MR Imaging using FOCUSS,"Magn Reson Med, vol. 57, pp. 764-775, April 2007.

[5] H. Jung, and J. C. Ye, "Motion Estimated and Compensated Compressed Sensing Dynamic Magnetic Resonance Imaging: What We Can Learn From Video Compression Techniques," International Journal of Imaging Systems and Technology, . vol 20, pp. 81-98, 18 May 2010.




 Acknowledgement
This work was supported in part by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD) (KRF-2007-313-D00593). This was also supported in part by grant No. M10530010002-08N3001-00210 from the Korea Ministry of Education, Science and Technology.