HSTAU Y. LIAO |
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Current research
interests
Image processing
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.
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 appears to have 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. Dental data courtesy of Maaria Rantala at PaloDEx Group. (Conventional means FBP algorithm with Hamming filter or ART algorithm.)
Sparse image representation for limited data tomography This is an adaptation to tomography of the principle of compressive sampling (Candes et. al.) and sparse image representation (Elad et. al.) via overlapping patches. By assuming sparsity of the patches with respect to a basis that in turn is being optimized, one can recover images that cannot be recovered by a total variation-based method, which is a popular regularization criterion. (Conventional means FBP algorithm with Hamming filter.)
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 with some parameters, which 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 all the above, this is just an implementation of a popular segmentation algorithm named "active contours without edges" (Chan and Vese). The goal is to locate aphids in digital pictures.
Manifold embedding and clustering 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.
Education 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 Publications H.Y. Liao and G. Sapiro, "Sparse
image representation for limited data tomography," accepted for the IEEE
International Symposium on Biomedical Imaging, 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,
116501, 2006. 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 (Ed.), 2004. 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.
Abstract H.Y. Liao, J. Fu, and J. Frank, "On the relationship between the resolution and the number of projections in single particle methods." 4th International Conference on Structural Analysis of Supramolecular Assemblies by Hybrid Methods, March 2008, Lake Tahoe, CA, USA. Submitted. Other conferences Structure Biology meeting, NESS, the University of Connecticut, Connecticut, 2007 Workshop on Discrete Tomography: Algorithms and Applications,
New York, NY, 2005 IPRPI, Inverse Problems at the Rensselaer Polytechnic
Institute, 2004, Troy, NY, 2004 Third International Congress on Electron Tomography, Rensselaerville, NY, 2004, 2004 The Ninth International Workshop on Combinatorial Image
Analysis, Palermo, Italy 2003 Fifth IEEE EMBS International Summer School on Biomedical
Imaging, Ile de Berder,
France, 2002 Mathematical Sciences Research Institute, Workshop on Inverse
Problems, Berkeley, CA, 2001 The Eighth International Workshop on Combinatorial Image
Analysis, Philadelphia, PA, 2001 Workshop on Discrete Tomography: Algorithms and Applications,
Siena, Italy, 2000 Exchange Program on Discrete Tomography, Department of
Informatics, University of Szeged, Szeged, Hungary, 2000 IX
Latin-Iberian-American Congress on Operations Research, Buenos Aires,
Argentina, 1998
I was involved in the development of SNARK05 : A Programming System for 2-D Image Reconstruction from Projections Awards
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 Languages Chinese
(Mandarin & Taiwanese), Spanish, and Russian (three months of intensive
course) |
