Share This Article:

New Approach for Limited-Angle Problems in Electron Microscope Based on Compressed Sensing

Abstract Full-Text HTML Download Download as PDF (Size:394KB) PP. 575-578
DOI: 10.4236/eng.2013.510B118    4,027 Downloads   4,719 Views   Citations

ABSTRACT

New advances within the recently rediscovered field of Compressed Sensing (CS) have opened for a great variety of new possibilities in the field of image reconstruction and more specifically in medical image reconstruction. In this work, a new approach using a CS-based algorithm is proposed and used in order to solve limited-angle problems (LAPs), like the ones that typically occur in computed tomography or electron microscope. This approach is based on a variant of the Robbins-Monro stochastic approximation procedure, developed by Egaziarian, using regularization by a spatially adaptive filter. This proposal consists on filling the gaps of missing or unobserved data with random noise and enabling a spatially adaptive denoising filter to regularize the data and reveal the underlying topology. This method was tested on different 3D transmission electron microscope datasets that presented different missing data artifacts (e.g, wedge or cone shape). The test results show a great potential for solving LAPs using the proposed technique.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Oliva, M. and Muhammed, H. (2013) New Approach for Limited-Angle Problems in Electron Microscope Based on Compressed Sensing. Engineering, 5, 575-578. doi: 10.4236/eng.2013.510B118.

References

[1] H. Peng and H. Stark, “Signal Recovery with Similarity Constraints,” Journal of the Optical Society of America A, Vol. 6, No. 6, 1989, pp. 844-851. http://dx.doi.org/10.1364/JOSAA.6.000844
[2] M. I. Sezan, “An Overview of Convex Projections Theory and Its Application to Image Recovery Problems, Ultramicroscopy,” Journal of the Optical Society of America A, Vol. 40, No. 1, 1992, pp. 55-67.
[3] M. I. Sezan and H. Stark, “Tomographic Image Recon?struction from Incomplete View Data by Convex Projections and Direct Fourier Inversion,” IEEE Transactions on Medical Imaging, Vol. 3, No. 2, 1984, pp. 91-98. http://dx.doi.org/10.1109/TMI.1984.4307661
[4] M. Fornasier, “A Convergent Overlapping Domain Decomposition Method for Total Variation Minimization,” Numerische Mathematik, Vol. 116, No. 4, 2010, pp. 645- 685. http://www.ricam.oeaw.ac.at/people/page/fornasier/
[5] A. Foi, K. Egiazarian and V. Katkovnik, “Compressed Sensing Image Reconstruction via Recursive Spatially Adaptive Filtering,” Image Processing, Vol. 1, 2007, pp. 549-552.
[6] D. L. Donoho, “Compressed Sensing,” IEEE Transactions on Information Theory, Vol. 52 No. 4, 2006, pp. 1289-1306.
[7] Y. Tsaig and D. L. Donoho, “Extensions of Compressed Sensing,” Signal Processing, Vol. 86, No. 3, 2006, pp. 549-571. http://dx.doi.org/10.1016/j.sigpro.2005.05.029
[8] J. Romberg, E. Candes and T. Tao, “Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information,” IEEE Transactions on Information Theory, Vol. 52, No. 2, 2006, pp. 489-509. http://dx.doi.org/10.1109/TIT.2005.862083
[9] D. L. Donoho and M. Elad, “Maximal Sparsity Represen?- tation via l1 Mini-mization,” Proceedings of the National Academy of Sciences of USA, Vol. 100, No. 5, 2008, pp. 2197-2202. http://dx.doi.org/10.1073/pnas.0437847100
[10] V. Katkovnik, K. Dabov, A. Foi and K. Egiazarian, “Image Denoising by Sparse 3d Transform-Domain Collaborative Filtering,” IEEE Transactions on Image Processing, Vol. 16, No. 8, 2007, pp. 2080-2095.
[11] Automated Molecular Imaging Group, Matlab mrc Speci?cation. http://ami.scripps.edu/software/mrctools/mrc_specification.php
[12] L. G. Ofverstedt, S. Masich, H. Rullgard, B. Danelholt and O. Oktem, “Simulation of Transmission Electron Microscope Images of Biological Specimens,” Journal of Microscopy, Vol. 243, No. 3, 2011, pp. 234-256.

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.