HSTAU Y. LIAO
In limited data tomography, with applications such as electron microscopy, medical imaging, industrial non-destructive testing, etc., the scanning views are within an angular range that is either limited or sparsely sampled. In these situations, conventional algorithms produce reconstructions with notorious artifacts. Below are some proposed solutions.
Currently I am working at Joachim Frank's Lab. I am looking into the classification problem, where noisy projections from several different structures coexist in a sample. See further down.
Mumford-Shah functional for limited data tomography
Here the M-S regularization is achieved via the Γ-convergence approximation, which yields both the unknown density values and the edge set. An alternated minimization algorithm can be used to optimize this functional. This is an example of a reconstruction from 30 projections. Compared to a conventional (FBP with Hamming filter) method, the M-S regularization has reduced the artifacts but also blurred the edges.
Gradual density recovery for limited data tomography
Artifacts in limited data problem can be treated as a "diffusion" of higher density regions into lower density regions. Thus, a gradual recovery of the densities from high to low values will reduce the artifacts and hence improve the contrast. These are reconstructions of a molar tooth from X-ray data, using 23, 15, and 8 projections. Note the two dark holes (pulp). No post-processing of the reconstructed images was applied. Data courtesy of Maaria Rantala at PaloDEx Group. ("Conventional" methods refer to FBP algorithm with Hamming filter and ART algorithm.) This work is also mentioned here.
Sparse image representation for limited data tomography
This is an adaptation to tomography of the principle of compressive sampling and sparse image representation via overlapping patches. By assuming sparsity of the patches with respect to a basis that in turn is being optimized, it is possible recover images that cannot be recovered by a total variation-based method, which is a popular regularization criterion. ("Conventional" method refers to FBP algorithm with Hamming filter.) This work is also mentioned in this site, which contains a vast collection of works on compressive sampling/sensing.
Direct labeling from a few projections for label reconstruction of macromolecule images
The aim is to produce a label (segmented) image, based only a few noisy projections. Conventional methods would first reconstruct the density image and then segment it. Using Markov random fields, it is possible however to directly produce a labeling from the projections. The idea is to model the set of images that are typical in the application by a MRF, whose parameters can be estimated from typical sample images. For example, here are some samples from different MRFs of binary (i.e., two-label) images in 2D and in 3D; and an example of reconstruction using only eight projections.
Active contours for segmenting images of aphids on leaves
Unlike the above, this is just an implementation of a popular segmentation algorithm known as "active contours without edges" (Chan and Vese). The goal is to locate aphids in digital pictures. Data courtesy of Martin Du Saire.
Geometric data analysis for electron microscopy of biological macromolecules
Projections of macromolecules at random unknown orientations are collected by electron microscopy. Typically, several classes of macromolecules (e.g., ribosome +/- EFG) coexist in a sample, which requires the separation of the classes before the reconstruction step. High dimensional data analysis tools have the potential for this task.
Ph.D., Computer Science, City University of New York, 2005 (Advisor: Gabor T. Herman)
M.S.E., Electrical Engineering, University of Pennsylvania, 2000 (Advisor: Gabor T. Herman)
Nuclear Engineer, Balseiro Institute, National Commission for Atomic Energy, UNC, Argentina
R. Bubinski, H.Y. Liao, and J. Frank, "Accelerating single-particle reconstruction algorithms on graphics processing units," in preparation
X. Agirrezabala, H.Y. Liao, E. Schreiner, J. Fu, R.F. Ortiz-Meoz, K. Schulten, R. Green, J. and Frank, "Evidence for the existence of intermediate states during translocation," in preparation
H.Y. Liao and J. Frank, "Classification by bootstrapping in single particle methods," IEEE International Symposium on Biomedical Imaging, pp. 169-172, 2010
J. Fu, Y. Hashem, I.Wower, J.Lei, H.Y. Liao, C. Zwieb, J Wower, and Joachim Frank, “Visualizing the transfer-messenger RNA as the ribosome resumes translation,” EMBO, vol. 29, pp. 3819 – 3825, 2010
H.Y. Liao and J. Frank, "Definition and estimation of resolution in single-particle reconstructions," Structure, vol. 18, pp.768-775, 2010
H.Y. Liao, Reconstruction of binary images using Gibbs Priors, LAP Lambert Academic Publishing 2009
H.Y. Liao and G.T. Herman, "Direct image reconstruction-segmentation, as motivated by electron microscopy," Advances in Discrete Tomography and Its Applications, in G.T. Herman and A. Kuba, Eds., Birkhauser, 2009
H.Y. Liao and G. Sapiro, "Sparse image representation for limited data tomography," IEEE International Symposium on Biomedical Imaging, pp. 1375-1378, Paris, France, 2008.
H.Y. Liao, "A gradually unmasking method for limited data tomography,” IEEE International Symposium on Biomedical Imaging, pp. 820-823, Arlington, VA, 2007.
I. Aganj, A. Bartesaghi, M. Borgnia, H.Y. Liao, G. Sapiro, and S. Subramaniam, “Regularization for inverting the Radon transform with wedge consideration,” IEEE International Symposium on Biomedical Imaging, pp. 217-220, Arlington, VA, 2007.
H.Y. Liao and G.T. Herman, "Direct image reconstruction-segmentation, as motivated by electron microscopy," Advances in Discrete Tomography and Its Applications, in G.T. Herman and A. Kuba (Eds.), Birkhauser, 2007.
H.Y. Liao and G.T. Herman, "A method for reconstructing label images from a few projections, as motivated by electron microscopy." Annals of Operations Research, vol. 148, pp. 117-132, 2006.
X. Fu, E. Knudsen, H.F. Poulsen, G.T. Herman, B.M. Carvalho,
and H.Y. Liao, "Optimized
algebraic reconstruction technique for generation of grain maps based on
three-dimensional x-ray diffraction (3DXRD)." Optical Engineering,
H.Y. Liao and G.T. Herman, "Discrete tomography with a very few views, using Gibbs priors and a Marginal Posterior Mode." Electronic Notes in Discrete Mathematics, vol. 20, 2005.
X. Fu, E. Knudsen, H.F. Poulsen, G.T. Herman, B.M. Carvalho,
and H.Y. Liao, "Optimization of an algebraic reconstruction technique
for generation of grain maps based on diffraction data." Proc. SPIE,
vol. 5535, pp. 261-273, Developments in X-Ray Tomography IV; Ulrich Bonse
H.Y. Liao and G.T. Herman, "Automated estimation of the parameters of Gibbs priors to be used in binary tomography." Discrete Applied Mathematics, vol. 139, pp. 149-170, 2004.
H.Y. Liao and G.T. Herman, "Tomographic reconstruction of label images from a few projections." Electronic Notes in Discrete Mathematics, vol. 12, 2003.
H.Y. Liao and G.T. Herman, "Reconstruction of label images as motivated by electron microscopy." Proc. IEEE 26th Northeast Bioengineering Conference, pp. 205-206, Philadelphia, PA, 2002.
M. Venere, H. Liao, and A. Clausse, "A genetic algorithm for adaptive tomography of elliptical objects." IEEE Signal Processing Letters, vol 7, pp. 176-178, 2000.
U.S. Patent 7,840,053 “System and Methods for Tomography Image Reconstruction”
Travel Award, IEEE 31st Northeast Bioengineering Conference, 2005
Mina Rees Fellowship, The Graduate Center, CUNY, 2004
Silver and bronze medals, 32nd-33rd International Mathematical Olympiad and the 5th-6th Iberian-American Mathematical Olympiad
Chinese (Mandarin & Taiwanese), Spanish, and Russian (three months of intensive course)