Dictionary-Learning-Based Reconstruction Method for Electron Tomography

Electron tomography usually suffers from so-called “missing wedge” artifacts caused by limited tilt angle range. An equally sloped tomography (EST) acquisition scheme (which should be called the linogram sampling scheme) was recently applied to achieve 2.4-angstrom resolution. On the other hand, a compressive sensing inspired reconstruction algorithm, known as adaptive dictionary based statistical iterative reconstruction (ADSIR), has been reported for X-ray computed tomography. In this paper, we evaluate the EST, ADSIR, and an ordered-subset simultaneous algebraic reconstruction technique (OS-SART), and compare the ES and equally angled (EA) data acquisition modes. Our results show that OS-SART is comparable to EST, and the ADSIR outperforms EST and OS-SART. Furthermore, the equally sloped projection data acquisition mode has no advantage over the conventional equally angled mode in this context.

[1]  Joseph F. Murray,et al.  Dictionary Learning Algorithms for Sparse Representation , 2003, Neural Computation.

[2]  Guohua Cao,et al.  Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems , 2011, Physics in medicine and biology.

[3]  Hengyong Yu,et al.  SART-Type Image Reconstruction from Overlapped Projections , 2011, Int. J. Biomed. Imaging.

[4]  Li Zhang,et al.  Total Variation Based Iterative Image Reconstruction , 2005, CVBIA.

[5]  E. Loli Piccolomini,et al.  A total variation regularization strategy in dynamic MRI , 2005, Optim. Methods Softw..

[6]  Lei Zhang,et al.  Low-Dose X-ray CT Reconstruction via Dictionary Learning , 2012, IEEE Transactions on Medical Imaging.

[7]  M. Jiang,et al.  Ordered-subset simultaneous algebraic reconstruction techniques (OS-SART) , 2004 .

[8]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[9]  Ge Wang,et al.  Few-view image reconstruction with dual dictionaries , 2012, Physics in medicine and biology.

[10]  J. Frank.  Electron tomography : methods for three-dimensional visualization of structures in the cell , 2005 .

[11]  G. Herman,et al.  Linograms in Image Reconstruction from Projections , 1987, IEEE Transactions on Medical Imaging.

[12]  Yuying Li,et al.  A computational algorithm for minimizing total variation in image restoration , 1996, IEEE Trans. Image Process..

[13]  Hengyong Yu,et al.  A soft-threshold filtering approach for reconstruction from a limited number of projections , 2010, Physics in medicine and biology.

[14]  Fabiana Zama,et al.  A total variation-based reconstruction method for dynamic MRI , 2008 .

[15]  Ronald R. Coifman,et al.  A Framework for Discrete Integral Transformations I-The Pseudopolar Fourier Transform , 2008, SIAM J. Sci. Comput..

[16]  J. Miao,et al.  Equally sloped tomography with oversampling reconstruction , 2005 .

[17]  Ronald R. Coifman,et al.  A Framework for Discrete Integral Transformations II-The 2D Discrete Radon Transform , 2008, SIAM J. Sci. Comput..

[18]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[19]  Ge Wang,et al.  Dual-dictionary learning-based iterative image reconstruction for spectral computed tomography application , 2012, Physics in medicine and biology.

[20]  A. Frangakis,et al.  The molecular architecture of cadherins in native epidermal desmosomes , 2007, Nature.

[21]  Frank Natterer,et al.  Mathematical methods in image reconstruction , 2001, SIAM monographs on mathematical modeling and computation.

[22]  S. Osher,et al.  Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM) , 2011, Inverse problems.

[23]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[24]  Joachim Frank,et al.  Electron Tomography , 1992, Springer US.

[25]  Jun Tian.  2 Computational and Mathematical Methods in Medicine , 2014 .

[26]  J. Miao,et al.  Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography. , 2008, Journal of structural biology.

[27]  P. Midgley,et al.  Embedded Nanostructures Revealed in Three Dimensions , 2005, Science.

[28]  E. Sidky,et al.  Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization , 2008, Physics in medicine and biology.

[29]  V. Lučić,et al.  Structural studies by electron tomography: from cells to molecules. , 2005, Annual review of biochemistry.

[30]  K. T. Block,et al.  Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint , 2007, Magnetic resonance in medicine.

[31]  A. Sali,et al.  The molecular sociology of the cell , 2007, Nature.