Research Highlight at Bio Imaging Signal Processing Lab

The main goal of BISPL is to develop new biomedical imaging applications of the compressed sensing that can revolutionize the imaging industry and greatly enhance our ability to monitor biological structures and processes. The imaging systems of our interests include existing modalities such as magnetic resonance imaging (MRI), x-ray computed tomography (CT) as well as emerging modalities such as near infrared spectroscopy (NIRS), cryo-electron microscopy, diffuse optical tomography, optical microscopy and etc. We are aiming at developing new type of imaging devices and sophisticated compressed sensing theory to address the many open problems in bio imaging area.

Near Infrared Spectroscopy (NIRS) for Brain Imaging

Near infrared spectroscopy (NIRS) is a non-invasive method to measure brain activity via changes in the degree of hemoglobin oxygenation through the intact skull. As optically measured hemoglobin signals strongly correlate with BOLD signals, simultaneous measurement using NIRS and fMRI promises a significant mutual enhancement of temporal and spatial resolution. In this research, we not only develop a new public domain statistical toolbox, called NIRS-SPM, but also apply our statistical analysis framework to cognitive fNIRS studies.

DYnamic MR imaging

In MRI, it is difficult to reconstruct dynamic images such as cardiac motion or fMRI BOLD signal without sacrificing the spatial and temporal resolution. In order to improve the spatio-temporal resolution, we have exploited the fact that the spatio-temporal supports of dynamic objects are sparse in frequency domain. Therefore, by improving the sparsity condition in spatio-temporal supports, we can retrieve the high resolution dynamic MRI images from very limited samples. We found that the FOCUSS algorithm proposed for EEG imaging can be effectively used for dynamic MR imaging, and applied for Cartesian and radial trajectory of MRI for brain and cardiac imaging applications.

Terahertz inverse scattering algorithm

Terahertz time-domain spectroscopy generates the broad-band light which ranges from 0.2THz~2THz (1x1012Hz ~ 0.3mm). This broad band light is transmitted through the volume space and is reflected at the target that we want to reconstruct. When the light interacts with objects, at the frequency domain, some components are transformed. This transformed wave is detected at detector's plane. The changing in the light can be interpreted as useful information about target's position and target's optical properties. These properties can be reconstructed by greedy algorithm based on compressed sensing(S-OMP). We can reconstruct the original volume through the S-OMP algorithm showing a high exact reconstruction ratio in simulation data. It opens the new modality of imaging the bio-sample in terahertz reflection tomography.

Diffuse Optical Tomography

The objective of optical diffusion imaging is to reconstruct the optical properties of cross-section of a highly scattering medium such as tissue, based on measurements of the scattered and attenuated optical energy. A major difficulty in optical imaging is, however, that the optical signal within tissue experiences significant scatter. More specifically, the photon path can be approximated using the diffusion equation. Note that inverse scattering problem is highly nonlinear due to the nonlinear coupling between the unknown coefficient and the photon flux in the diffusion equation. The goal of this research is to develop a novel non-iterative exact reconstruction algorithm using simultaneous sparse representation. Our reconstruction theory is based on sparsity. The problem can be solved using various simultaneous sparse approximation algorithms such as simultaneous orthogonal matching pursuit(S-OMP), and the unknown scattering coefficients can be then exactly calculated based on a simple two step approach without calculating a diffusion equation.

EM (Electron Microscopy) 3-D Reconstruction of Macromolecules

The model free 3-D reconstruction of helical structure is possible from a single view by exploiting the symmetry and sparsity. Helical symmetry provides specific number of symmetric views from only single view. However, the number of symmetric views is not sufficient for accurate 3-D reconstruction. To overcome the resolution loss due to the sparse views, we develop an iterative reconstruction method based on compressed sensing by exploiting the sparsity of structures. We can show that our algorithm provided very accurate reconstruction.

Exact single Channel Blind Image Deconvolution

The multichannel exact blind image deconvolution theory tells us that exact recovery of unknown blur kernels is possible from multiple measurements of an identical scene through distinct blur channels. There often exist obstacles in obtaining multiple distinct blur measurements in many biological applications. In this research, we suggest the single channel blind image deconvolution based on the radial symmetry of PSF, which eliminates the need of multiple blur measurements, but still guarantees an accurate estimation of the blurring kernel.

Multi-energy X-ray Material Decomposition

The physical compositions of human body such as tissue, bone, and muscle can be possibly decomposed using monochromatic X-ray beams with various energy levels based on the difference of attenuation coefficient. However, in practice, it is hard to generate the idealized monochromatic x-ray beams. Therefore, we are willing to develop the novel mathematical method that can effectively decompose each material under realistic situation.

Compressed Sensing Theory for Bio-Imaging Problem

The multiple measurement vector (MMV) problem refers the identification problem of unknown multiple sparse input vectors that share the common non-zero supports. This problem has many practical applications such as distributed compressed sensing, target localization from electromagnetic scattering from multiple illuminations, diffuse optical tomography, and etc. Surprisingly, considering the practical significance, relatively limited number of theoretical results are available for MMV compared to its single measurment vector (SMV) counterpart. For example, the explicit performance dependency on the number of measurement vectors has been formally shown only for l0 identification and some specialized greedy algorithms. Our research interest is to completely describe the geometry of the MMV problem that has not been addressed. Especially, we're trying to derive the tighter sparsity bound on l1 identification problem, simultaneous orthogonal matching pursuit and etc.