Beyond Nyquist: Two bio-imaging applications of compressed sensing

Recent theory of compressed sensing (CS) informs us that near-exact recovery of an unknown sparse signal is 
possible from a very limited number of Fourier samples by solving a convex L1 optimization problem.
In this presentation, we discuss two applications of this theory: dynamic MRI and electron microscopy.

The dynamic MR imaging of time-varying objects, such as beating hearts or brain hemodynamics, requires
a significant reduction of the data acquisition time without sacrificing spatial resolution.  Recently, model-based
reconstruction methods called k–t BLAST and k–t SENSE have been proposed which largely overcome the 
drawbacks of the conventional dynamic imaging methods without a priori knowledge of the spectral support. 
Another recent approach called k–t SPARSE also does not require exact knowledge of the spectral support. 
However, unlike k–t BLAST/SENSE, k–t SPARSE employs the so-called compressed sensing (CS)
theory rather than using training. The main contribution of this paper is a new theory and algorithm that unifies 
the abovementioned approaches while overcoming their drawbacks. Specifically, we show that the celebrated 
k–t BLAST/SENSE are the special cases of our algorithm called k-t FOCUSS, which is asymptotically optimal 
from the CS theory perspective. Experimental results show that k-t FOCUSS can successfully reconstruct a high 
resolution cardiac sequence and functional MRI data even from severely limited k–t samples, without incurring 
aliasing artifacts often observed in conventional methods.

In the second part of this talk, we will discuss about a novel compressed sensing shape estimation framework 
and a computational algorithm for binary star shape objects, whose radius functions belong to the space of 
bounded-variation functions.  This type of problem is often encountered in single particle reconstruction problem
using electron microscopy under negative staining.  In contrast with standard compressed sensing, the new 
approach involves directly reconstructing the shape boundary under sparsity constraint of the boundary. This is 
done by converting the standard pixel based reconstruction approach into estimation of a non-parametric shape 
boundary on a wavelet basis. This results in an L1 minimization under a nonlinear constraint, which makes the 
optimization problem nonconvex. We solve the problem by successive linearization and application of compressed 
sensing, which significantly reduces the number of sampling requirements as well as the computational burden. 
Fourier imaging simulation results demonstrate that high quality reconstruction can be quickly obtained from a 
very limited number of samples. Furthermore, the algorithm outperforms the standard compressed sensing 
reconstruction approach using the total variation norm.

Short-Biography
Jong Chul Ye received the B.Sc. and M.Sc. degrees with honors from Seoul National University, Seoul, Korea, 
in 1993 and 1995, respectively, and the Ph.D. degree from the School of Electrical and Computer Engineering, 
Purdue University, West Lafayette, IN, in 1999. He was with the X-ray CT Technology Group at GE Global 
Research Center (2003 to 2004) and Philips Research, Briarcliff Manor, NY (2001 to 2003), and Image Science 
Lab. at Polaroid Corp. (2001) as a senior research member. He was also with Coordinated Science Laboratory, 
University of Illinois at Urbana-Champaign, Urbana (1999 to 2001) as a postdoc. In 2004, he joined the Korea 
Advanced Institute of Science and Technology (KAIST), Daejon, Korea; where he is currently an Assistant 
Professor with the Department of Bio and Brain Engineering, and jointly appointed at Dept. of Electrical and 
Computer Engineering. His current research interests lies in applying advanced signal processing theory to 
various  bio-imaging applications such as MRI, electron microscopy, diffuse optical tomography, NIRS etc.