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.
 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.
 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.
 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.
 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.
 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.
Patch-based low-rank regularization for dynamic MRI
An image is called self-similar when it is similar to a part of itself. An dynamic image inherently has self-similar structure because of repetition of similar images along time.The self-similiarity of an image can be used as a prior for a dynamic image reconstruction problem. To exploit the self-similar structure of the image, the image is divided into smaller image patches, and the similar patches are concatenated as the matrices, which have low-rank. Similar patches are retrieved spatiotemporally (Figure.1). The proposed algorithm provides improved motion reconstruction than conventional algorithms, which use the fixed sparsifying transforms along the time dimension.
The proposed algorithm shows the clearer fine detailed structures like edge than conventional algorithms. It is also effective even when the measured data is corrupted with noise.
 Huisu Yoon and Jong Chul Ye, "Motion Estimation/Compensated Compressed Sensing using Patch-Based Low Rank Penalty", Wavelets and Sparsity XV, San Diego, USA, August 2013.
 Huisu Yoon, Kyung Sang Kim and Jong Chul Ye, "Motion residual reconstruction using low rank property of similarity patches in motion compensated compressed sensing dynamic MRI", International Society of Magnetic Resonance in medicine (ISMRM) 21st Annual meeting & exhibition, Salt Lake City, Utah, USA, April, 2013
Compressed Sensing for CEST Imaging
Chemical Exchange Saturation Transfer (CEST) imaging is a recent technique with growing interest that allows for molecular imaging. This technique can detect low-concentration compounds with exchangeable protons through saturation transfer to water signal. CEST may be combined with a 3D gradient echo based readout to minimize distortion and to avoid slice-dependent saturation frequency variations. Since CEST requires the usage of a relatively long saturation pulse often for a series of multiple radiation frequencies, combination with 3D gradient echo readout is potentially limited in terms of spatial coverage. One potential approach to overcome this limitation is to use compressed sensing (CS). We obtained in vivo 3D image results using k-t FOCUSS for 3D CEST imaging with balanced steady-state free precession (bSSFP) and fast imaging with steady-state precession (FISP) in a 3T human MR scanner. Experimental results show that CS acceleration by a factor of 4 works well for both 3D bSSFP-CEST and 3D FISP-CEST and improves the z-spectrum compared to parallel imaging method, which confirms that combination of CS may be a good solution for 3D- CEST imaging.
Acceleration of MR parameter mapping
Mapping is one of valuable MRI application for diagnosis of various diseases in clinic. Especially, T2 prime (T2') mapping is an application of parametric MRI technique for diagnosis of brain diseases such as ischemic stroke and occlusive carotid disease. Recently, T2’ imaging was proposed as a better way to predict infarct growth in acute stroke than Diffusion Weighted Imaging (DWI) which was commonly used. Because T2’ map is T2* mapping with correction for T2 relaxation effects, it may provide useful information of blood oxygenation that is not affected by signal changes caused by gliosis or edema. However, the quantitative measure of parameter maps with high resolution requires the acquisition of multiple images using different sequence parameters such as echo time (TE). That is usually associated with long acquisition times although time saving is the most important thing in acquisition of MRI in acute ischemic stroke because therapy should be given to patients as soon as possible.Therefore, to reduce the acquisition time of MR data, we use a compressed sensing algorithm using patch based low rank penalty.