The Annals of Applied Statistics

Two-level structural sparsity regularization for identifying lattices and defects in noisy images

Xin Li, Alex Belianinov, Ondrej Dyck, Stephen Jesse, and Chiwoo Park

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Abstract

This paper presents a regularized regression model with a two-level structural sparsity penalty applied to locate individual atoms in a noisy scanning transmission electron microscopy image (STEM). In crystals, the locations of atoms is symmetric, condensed into a few lattice groups. Therefore, by identifying the underlying lattice in a given image, individual atoms can be accurately located. We propose to formulate the identification of the lattice groups as a sparse group selection problem. Furthermore, real atomic scale images contain defects and vacancies, so atomic identification based solely on a lattice group may result in false positives and false negatives. To minimize error, model includes an individual sparsity regularization in addition to the group sparsity for a within-group selection, which results in a regression model with a two-level sparsity regularization. We propose a modification of the group orthogonal matching pursuit (gOMP) algorithm with a thresholding step to solve the atom finding problem. The convergence and statistical analyses of the proposed algorithm are presented. The proposed algorithm is also evaluated through numerical experiments with simulated images. The applicability of the algorithm on determination of atom structures and identification of imaging distortions and atomic defects was demonstrated using three real STEM images. We believe this is an important step toward automatic phase identification and assignment with the advent of genomic databases for materials.

Article information

Source
Ann. Appl. Stat. Volume 12, Number 1 (2018), 348-377.

Dates
Received: April 2017
Revised: August 2017
First available in Project Euclid: 9 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1520564476

Digital Object Identifier
doi:10.1214/17-AOAS1096

Keywords
Sparse regression structural sparsity lattice group structural evaluation of materials image data analysis

Citation

Li, Xin; Belianinov, Alex; Dyck, Ondrej; Jesse, Stephen; Park, Chiwoo. Two-level structural sparsity regularization for identifying lattices and defects in noisy images. Ann. Appl. Stat. 12 (2018), no. 1, 348--377. doi:10.1214/17-AOAS1096. https://projecteuclid.org/euclid.aoas/1520564476


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References

  • Adler, S. B. (2004). Factors governing oxygen reduction in solid oxide fuel cell cathodes. Chem. Rev. 104 4791–4843.
  • Bay, H., Ess, A., Tuytelaars, T. and Van Gool, L. (2008). Speeded-up robust features (SURF). Comput. Vis. Image Underst. 110 346–359.
  • Belianinov, A., He, Q., Kravchenko, M., Jesse, S., Borisevich, A. and Kalinin, S. V. (2015). Identification of phases, symmetries and defects through local crystallography. Nat. Commun. 6 7801.
  • Borisevich, A. Y., Chang, H. J., Huijben, M., Oxley, M. P., Okamoto, S., Niranjan, M. K., Burton, J., Tsymbal, E., Chu, Y.-H., Yu, P. et al. (2010a). Suppression of octahedral tilts and associated changes in electronic properties at epitaxial oxide heterostructure interfaces. Phys. Rev. Lett. 105 087204.
  • Borisevich, A., Ovchinnikov, O. S., Chang, H. J., Oxley, M. P., Yu, P., Seidel, J., Eliseev, E. A., Morozovska, A. N., Ramesh, R., Pennycook, S. J. et al. (2010b). Mapping octahedral tilts and polarization across a domain wall in BiFeO3 from Z-contrast scanning transmission electron microscopy image atomic column shape analysis. ACS Nano 4 6071–6079.
  • Bradzil, J. F. (2010). Acrylonitrile. In Kirk–Othmer Encyclopedia of Chemical Technology. Wiley, New York.
  • Bright, D. S. and Steel, E. B. (1987). Two-dimensional top hat filter for extracting spots and spheres from digital images. J. Microsc. 146 191–200.
  • Chang, H. J., Kalinin, S. V., Morozovska, A. N., Huijben, M., Chu, Y.-H., Yu, P., Ramesh, R., Eliseev, E. A., Svechnikov, G. S., Pennycook, S. J. et al. (2011). Atomically resolved mapping of polarization and electric fields across ferroelectric/oxide interfaces by Z-contrast imaging. Adv. Mater. 23 2474–2479.
  • Chatterjee, S., Steinhaeuser, K., Banerjee, A., Chatterjee, S. and Ganguly, A. (2012). Sparse group lasso: Consistency and climate applications. In Proceedings of the 2012 SIAM International Conference on Data Mining 47–58. SIAM, Philadelphia, PA.
  • Dima, A., Bhaskarla, S., Becker, C., Brady, M., Campbell, C., Dessauw, P., Hanisch, R., Kattner, U., Kroenlein, K., Newrock, M. et al. (2016). Informatics infrastructure for the materials genome initiative. JOM 68 2053–2064.
  • Genovese, C. R., Jin, J., Wasserman, L. and Yao, Z. (2012). A comparison of the lasso and marginal regression. J. Mach. Learn. Res. 13 2107–2143.
  • He, J., Borisevich, A., Kalinin, S. V., Pennycook, S. J. and Pantelides, S. T. (2010). Control of octahedral tilts and magnetic properties of perovskite oxide heterostructures by substrate symmetry. Phys. Rev. Lett. 105 227203.
  • He, Q., Woo, J., Belianinov, A., Guliants, V. V. and Borisevich, A. Y. (2015). Better catalysts through microscopy: Mesoscale M1/M2 intergrowth in molybdenum–vanadium based complex oxide catalysts for propane ammoxidation. ACS Nano 9 3470–3478.
  • Huang, J., Zhang, T. and Metaxas, D. (2011). Learning with structured sparsity. J. Mach. Learn. Res. 12 3371–3412.
  • Hughes, J., Fricks, J. and Hancock, W. (2010). Likelihood inference for particle location in fluorescence microscopy. Ann. Appl. Stat. 4 830–848.
  • Jenatton, R., Audibert, J.-Y. and Bach, F. (2011). Structured variable selection with sparsity-inducing norms. J. Mach. Learn. Res. 12 2777–2824.
  • Jia, C.-L., Nagarajan, V., He, J.-Q., Houben, L., Zhao, T., Ramesh, R., Urban, K. and Waser, R. (2007). Unit-cell scale mapping of ferroelectricity and tetragonality in epitaxial ultrathin ferroelectric films. Nat. Mater. 6 64–69.
  • Jia, C., Mi, S., Faley, M., Poppe, U., Schubert, J. and Urban, K. (2009). Oxygen octahedron reconstruction in the SrTiO3/LaAlO3 heterointerfaces investigated using aberration-corrected ultrahigh-resolution transmission electron microscopy. Phys. Rev. B 79 081405.
  • Jia, C.-L., Urban, K. W., Alexe, M., Hesse, D. and Vrejoiu, I. (2011). Direct observation of continuous electric dipole rotation in flux-closure domains in ferroelectric Pb(Zr,Ti)O3. Science 331 1420–1423.
  • Kim, Y.-M., He, J., Biegalski, M. D., Ambaye, H., Lauter, V., Christen, H. M., Pantelides, S. T., Pennycook, S. J., Kalinin, S. V. and Borisevich, A. Y. (2012). Probing oxygen vacancy concentration and homogeneity in solid-oxide fuel-cell cathode materials on the subunit-cell level. Nat. Mater. 11 888–894.
  • Kim, Y.-M., Kumar, A., Hatt, A., Morozovska, A. N., Tselev, A., Biegalski, M. D., Ivanov, I., Eliseev, E. A., Pennycook, S. J., Rondinelli, J. M. et al. (2013). Interplay of octahedral tilts and polar order in BiFeO3 films. Adv. Mater. 25 2497–2504.
  • Kim, Y.-M., Morozovska, A., Eliseev, E., Oxley, M. P., Mishra, R., Selbach, S. M., Grande, T., Pantelides, S., Kalinin, S. V. and Borisevich, A. Y. (2014). Direct observation of ferroelectric field effect and vacancy-controlled screening at the BiFeO3/La$Sr$MnO3 interface. Nat. Mater. 13 1019–1025.
  • Liu, J. and Ye, J. (2010). Moreau–Yosida regularization for grouped tree structure learning. In Advances in Neural Information Processing Systems 1459–1467.
  • Mody, C. C. M. (2011). Instrumental Community: Probe Microscopy and the Path to Nanotechnology. MIT Press, Cambridge, MA.
  • Nellist, P. and Pennycook, S. (2000). The principles and interpretations of annular dark-field Z-contrast imaging. Adv. Imaging Electron Phys. 113 148–204.
  • Nelson, C. T., Winchester, B., Zhang, Y., Kim, S.-J., Melville, A., Adamo, C., Folkman, C. M., Baek, S.-H., Eom, C.-B., Schlom, D. G. et al. (2011). Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces. Nano Lett. 11 828–834.
  • Rezatofighi, S. H., Hartley, R. and Hughes, W. E. (2012). A new approach for spot detection in total internal reflection fluorescence microscopy. In 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI) 860–863.
  • Sage, D., Neumann, F. R., Hediger, F., Gasser, S. M. and Unser, M. (2005). Automatic tracking of individual fluorescence particles: Application to the study of chromosome dynamics. IEEE Trans. Image Process. 14 1372–1383.
  • Sang, X., Lupini, A. R., Unocic, R. R., Chi, M., Borisevich, A. Y., Kalinin, S. V., Endeve, E., Archibald, R. K. and Jesse, S. (2016a). Dynamic scan control in STEM: Spiral scans. Adv. Struct. Chem. Imaging 2 6.
  • Sang, X., Xie, Y., Lin, M.-W., Alhabeb, M., Van Aken, K. L., Gogotsi, Y., Kent, P. R., Xiao, K. and Unocic, R. R. (2016b). Atomic defects in monolayer titanium carbide (Ti3C2T$) MXene. ACS Nano 10 9193–9200.
  • She, Y. (2009). Thresholding-based iterative selection procedures for model selection and shrinkage. Electron. J. Stat. 3 384–415.
  • She, Y. (2010). Sparse regression with exact clustering. Electron. J. Stat. 4 1055–1096.
  • She, Y., Wang, J., Li, H. and Wu, D. (2013). Group iterative spectrum thresholding for super-resolution sparse spectral selection. IEEE Trans. Signal Process. 61 6371–6386.
  • Shiju, N. R. and Guliants, V. V. (2009). Recent developments in catalysis using nanostructured materials. Appl. Catal., A Gen. 356 1–17.
  • Simon, N., Friedman, J., Hastie, T. and Tibshirani, R. (2013). A sparse-group lasso. J. Comput. Graph. Statist. 22 231–245.
  • Slawski, M. and Hein, M. (2013). Non-negative least squares for high-dimensional linear models: Consistency and sparse recovery without regularization. Electron. J. Stat. 7 3004–3056.
  • Smal, I., Niessen, W. and Meijering, E. (2008). A new detection scheme for multiple object tracking in fluorescence microscopy by joint probabilistic data association filtering. In 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro 264–267.
  • Vasudevan, R. K., Belianinov, A., Gianfrancesco, A. G., Baddorf, A. P., Tselev, A., Kalinin, S. V. and Jesse, S. (2015). Big data in reciprocal space: Sliding fast Fourier transforms for determining periodicity. Appl. Phys. Lett. 106 091601.
  • Vincent, L. (1993). Morphological grayscale reconstruction in image analysis: Applications and efficient algorithms. IEEE Trans. Image Process. 2 176–201.
  • Yankovich, A. B., Berkels, B., Dahmen, W., Binev, P., Sanchez, S. I., Bradley, S. A., Li, A., Szlufarska, I. and Voyles, P. M. (2014). Picometre-precision analysis of scanning transmission electron microscopy images of platinum nanocatalysts. Nat. Commun. 5 4155.
  • Yuan, M. and Lin, Y. (2006). Model selection and estimation in regression with grouped variables. J. R. Stat. Soc. Ser. B. Stat. Methodol. 68 49–67.