
Representative Research Outputkt FOCUSS: Compressed Sensing Dynamic MRIIn order to acquire timevarying objects such as beating hearts or brain hemodynamics using MRI, a significant reduction of the data acquisition time is required. Classical MR imaging approaches are all constrained by the Nyquist sampling theory, so such acceleration results in aliasing artifacts. Modelbased reconstruction methods such as kt BLAST may have some advantages but still suffer from blurring or signal nulling artifacts.
This paper identified the kt BLAST as a suboptimal approximation of our compressed sensing dynamic MRI algorithm called kt FOCUSS, which is optimal from a compressed sensing perspective (See Figure~\ref{fig:ktFOCUSS}). Moreover, we extend kt FOCUSS to amore general framework with prediction and residual encoding, where the prediction provides an initial estimate and the residual encoding takes care of the remaining residual signals. Among various prediction schemes, we showed that a motion estimation/compensation scheme significantly sparsifies the residual signals. Using the world's first {\em in vivo} pulse sequence implementation, we showed that excellent reconstruction can be achieved even from severely limited kt samples without aliasing artifacts. Significance This work is one of the most oftencited papers on compressed sensing dynamic magnetic resonance (MR) imaging. The idea of using a reweighted norm algorithm known as FOCUSS originated from our early work on projection reconstruction MR imaging from limited radial spokes , whose success inspired us to exploit the transform domain sparsity in the kt FOCUSS algorithm. This paper generalized our previous kt FOCUSS framework using a new paradigm with prediction and residual encoding, and demonstrated its effectiveness using the world's first in vivo pulse sequence implementation. We further extended the idea to radial $k$space trajectory MR acquisition again with another in vivo pulse sequence implementation. Later, with the collaboration of radiologists in New York University Hospital, we demonstrated that kt FOCUSS provides significant improved reconstruction quality in T2 parameter mapping imaging even at higher acceleration, compared to the golden standard parallel imaging . Since the first publication of kt FOCUSS in 2007, a flurry of papers has been published by independent research teams all over the world comparing their algorithms with kt FOCUSS, bringing to over 400 the total number of citations of my kt FOCUSS papers. In 2009, the effectiveness of kt FOCUSS was recognized unanimously recognized by radiologists from various leading hospitals and was named 1st Place Winner at the Reconstruction Challenge of the ISMRM (International Society for Magnetic Resonance in Medicine) Workshop}} on Data Sampling and Image Reconstruction. In addition, the intellectual properties related to kt FOCUSS have been successfully transferred to industries with undisclosed amount royalties, which is the largest amount in Departmental history. NIRSSPM: Quantitative Statistical Analysis for functional Near Infrared Spectroscopy (fNIRS) in Brain Study
Significance Since the web release of NIRSSPM , more than 4000 downloads have been performed from countless institutions, and have been employed by various fNIRS systems vendors worldwide. For example, Shimadzu Co. of Japan graciously invited me to Tokyo to open the first NIRSSPM short course for their Shimadzu fNIRS users using NIRSSPM. Furthermore, I am proud that NIRSSPM is the only Korean neuroimaging toolbox registered in Neuroimaging Informatics Tools and Resources Clearinghouse (NITRC), the NITRC being funded by the National Institutes of Health Blueprint for Neuroscience Research Thanks to my contributions in the fNIRS community, Another important features of NIRSSPM is a new signal detrending method using waveletMDL detrending. A waveletbased detrending algorithm was used to decompose NIRS measurements into global trends, hemodynamic signals, and uncorrelated noise on distinct scales . We have also demonstrated that NIRSSPM can be used to calculate the cerebral metaloblic rate of oxygen (CMRO2), which is one of the key biomarkers to differentiate subcortical vascular dementia patients . CSMUSIC: Mathematical Theory for Joint Sparse RecoveryThe multiple measurement vector (MMV) problem addresses the identification of unknown input vectors that share common sparse support. Even though MMV problems have been traditionally addressed within the context of sensor array signal processing, the recent trend is to apply compressive sensing (CS)
due to its ability to estimate sparse support even with an insufficient number of snapshots, in which case classical array signal processing fails. However, CS guarantees accurate recovery in a probabilistic manner, which often shows inferior performance in the regime where the traditional array signal processing approaches succeed. The apparent dichotomy between the probabilistic CS and deterministic sensor array signal processing has not been fully understood. The main contribution of this paper is {\bf\uline{to reveal the fundamental geometry of the MMV problem called a generalized MUSIC criterion that links CS and array signal processing. More specifically, as shown in Fig.~\ref{fig:cmusicgeo}, for rank deficiency measurement vectors, the true support vector $\ab_j$ is not orthogonal to the standard noise subspace from the multiple signal classification (MUSIC) algorithm ($R(Q)$). However, if we augment partial support $A_{I_{kr}}$ and calculate its orthogonal complement the true support $\ab_j$ now becomes orthogonal to the new subspace. The discovered fundamental geometry suggests a natural hybridization of compressed sensing and array signal processing, in which partial supports are found using compressed sensing and the remaining the supports are found using the generalized MUSIC criterion. Using a large system MMV model, we show that our compressive MUSIC requires a smaller number of sensor elements for accurate support recovery than the existing CS methods and that it can approach the optimal sampling rate with a finite number of snapshots even in cases where the signals are linearly dependent. Significance This novel mathematical theory on the MMV problem has a significant impact in many realworld medical imaging problems such as Electroencephalography (EEG) or Magnetoencephalography (MEG), and diffuse optical tomography. For example, in diffuse optical tomography (DOT) , due to the diffusive nature of light propagation, the problem is severely illconditioned and highly nonlinear. Even though nonlinear iterative methods have been commonly used, they are computationally complex especially for three dimensional imaging. The main contribution of is to formulate the imaging problem as a joint sparse recovery problem in a compressive sensing framework and to propose a novel noniterative and exact inversion algorithm that achieves the optimality as the measurement rank increases to the unknown sparsity level. The algorithm is based on the generalized MUSIC criterion, which exploits the advantages of both compressive sensing and array signal processing. Simulation results confirm that the new algorithm outperforms the existing algorithms and reliably reconstructs the optical inhomogeneities. 