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

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.

[1]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[2]  Henry Stark,et al.  Signal recovery with similarity constraints , 1989 .

[3]  H. RULLGÅRD,et al.  Simulation of transmission electron microscope images of biological specimens , 2011, Journal of microscopy.

[4]  Yong Cheng,et al.  Comments on "Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering" , 2011, IEEE Trans. Image Process..

[5]  M. Ibrahim Sezan,et al.  An overview of convex projections theory and its application to image recovery problems , 1992 .

[6]  Karen O. Egiazarian,et al.  Compressed Sensing Image Reconstruction Via Recursive Spatially Adaptive Filtering , 2007, 2007 IEEE International Conference on Image Processing.

[7]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Yaakov Tsaig,et al.  Extensions of compressed sensing , 2006, Signal Process..

[9]  Carola-Bibiane Schönlieb,et al.  A convergent overlapping domain decomposition method for total variation minimization , 2009, Numerische Mathematik.

[10]  D. Donoho,et al.  Maximal Sparsity Representation via l 1 Minimization , 2002 .

[11]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

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

[13]  M. Sezan,et al.  Tomographic Image Reconstruction from Incomplete View Data by Convex Projections and Direct Fourier Inversion , 1984, IEEE Transactions on Medical Imaging.