Convex optimization and greedy iterative algorithms for dictionary learning in the presence of Rician noise

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    Compressive Sensing (CS) is the emerging trend of recovering signal/image accurately from samples acquired at a rate far below the Nyquist rate. MR imaging provides a natural fit for applying CS as they can be sparsely represented in the transform domain. Magnitude MR images are corrupted by noise which follows Rician distribution and is difficult to remove as it is image dependent. Sparse coding is an important stage in dictionary learning. In this paper an attempt is being made to bring out a sparse coding technique which can provide better reconstruction in the presence of Rician noise. Greedy iterative algorithms and convex solutions are widely used for sparse coding. In the present work, performance of greedy algorithms, namely, Orthogonal Matching Pursuit (OMP) and Compressive Sampling Matching Pursuit (CoSaMP) have been evaluated and compared with convex techniques viz. Basis Pursuit (BP) and Least Absolute Shrinkage and Selection Operator (LASSO) in the sparse coding stage of an adaptive patch-based dictionary learning. Experiments have been carried out by varying Rician noise level from 0 to 30 and sparsity threshold per patch on MR images, acquired by employing various sampling schemes. Results show that greedy algorithms achieve higher PSNR and have very high computational speed compared to convex techniques when the MR images are corrupted with Rician noise.



  • Keywords

    Compressive Sensing; Convex Techniques; Greedy Iterative Algorithms; Magnetic Resonance Imaging.

  • References

      [1] Saiprasad Ravishankar, and Yoram Bresler, “MR Image Reconstruction from Highly Undersampled k-Space Data by Dictionary Learning”, IEEE Transactions on Medical Imaging, Vol. 30, No. 5, pp. 1028-1041, May 2011.

      [2] M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, “Compressed sensing MRI”, IEEE Signal Processing Mag., Mar. 2008, vol. 25, no. 2, pp. 72–82.

      [3] Saad Qaisar, Rana Muhammad Bilal, Wafa Iqbal, Muqaddas Naureen, and Sungyoung Lee, “Compressive Sensing: From Theory to Applications, a Survey”, Journal of Communications and Networks, October 2013, Vol. 15, No. 5.

      [4] J. Tropp, and A. C. Gilbert, “Signal Recovery from Random Measurements via Orthogonal Matching Pursuit”, IEEE Transactions on Information Theory, 2007, vol. 53, no.12, pp: 4655-4666.

      [5] D. Needell and J.A. Tropp., "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples". Communications of the ACM, vol. 53, no. 12, December 2010, pp: 93-100.

      [6] Scott Shaobing Cheny, David L. Donohoz, And Michael A. Saunders, “Atomic Decomposition by Basis Pursuit”, Society for Industrial and Applied Mathematics, 1998, Vol. 20, No. 1, pp. 33-61.

      [7] Emmanuel Cand`es and Justin Romberg, “ -magic: Recovery of Sparse Signals via Convex Programming”, Caltech, October 2005.

      [8] R. Tibshirani, “Regression shrinkage and selection via the lasso”, J. R. Statist. Soc. B, 1996, vol. 58, pp. 267–288.

      [9] David Donoho, Victoria Stodden and Yaakov Tsaig, About SparseLab, Stanford University, Version .100, May 2006.

      [10] M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. Signal Process., Nov. 2006, vol. 54, no. 11, pp. 4311–4322.

      [11] M.V.R. Manimala, C.D. Naidu and M. N. Giriprasad, “Sparse Recovery Algorithms Based on Dictionary Learning for MR Image Reconstruction”, IEEE 2016 International Conference on Wireless Networks, Signal Processing and Networking, March 2016, pp. 1354-1360.

      [12] Gudbjartsson H, Patz S., “The Rician Distribution on Noisy MRI Data”, Magn Reson Med 1995, vol. 34, pp: 910-914.

      [13] Gilles Hennenfent and Felix J. Herrmann, “Simply denoise: Wavefield reconstruction via jittered undersampling”, Geophysics, May-June 2008, Vol. 73, No. 3, P. V19–V28.

      [14] Yang et al., “Brain MR image denoising for Rician noise using pre-smooth non-local means filter”, BioMedical Engineering OnLine 2015.

      [15] Javier Portilla, Antonio Tristan-Vega, Ivan W. Selesnick, “Efficient and Robust Image Restoration using Multiple-Feature L2-relaxed Sparse Analysis Priors”, IEEE Transactions on Image Processing, December 2015, Vol. 24, No. 12, pp. 5046-5059.

      [16] Suyash P. Awate and Ross T. Whitaker, “Feature-Preserving MRI Denoising: A Nonparametric Empirical Bayes Approach”, IEEE Transactions on Medical Imaging, September 2007, Vol. 26, No. 9, pp. 1242-1255.

      [17] Yue Huangy, John Paisleyy, Qin Lin, Xinghao Dingz, Xueyang Fu and Xiao-ping Zhang, “Bayesian Nonparametric Dictionary Learning for Compressed Sensing MRI”, IEEE Transactions on Image Processing, Dec. 2014, Vol. 23, No. 12, pp:5007-5019.




Article ID: 15768
DOI: 10.14419/ijet.v7i4.15768

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.