Commenced in January 2007
Paper Count: 32119
Sparse-View CT Reconstruction Based on Nonconvex L1 − L2 Regularizations
Abstract:The reconstruction from sparse-view projections is one of important problems in computed tomography (CT) limited by the availability or feasibility of obtaining of a large number of projections. Traditionally, convex regularizers have been exploited to improve the reconstruction quality in sparse-view CT, and the convex constraint in those problems leads to an easy optimization process. However, convex regularizers often result in a biased approximation and inaccurate reconstruction in CT problems. Here, we present a nonconvex, Lipschitz continuous and non-smooth regularization model. The CT reconstruction is formulated as a nonconvex constrained L1 − L2 minimization problem and solved through a difference of convex algorithm and alternating direction of multiplier method which generates a better result than L0 or L1 regularizers in the CT reconstruction. We compare our method with previously reported high performance methods which use convex regularizers such as TV, wavelet, curvelet, and curvelet+TV (CTV) on the test phantom images. The results show that there are benefits in using the nonconvex regularizer in the sparse-view CT reconstruction.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1130109Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 974
 Brenner DJ J., Hall EJ.: Computed tomography: an increasing source of radiation exposure. N Engl J Med. 357(22), 2277–2284 (2007).
 Natarajan, B.K.: Sparse approximate solutions to linear systems. SIAM J. Com- put., 227234 (1995).
 Goldstein T., Osher S.:The split Bregman method for L1 regular- ized problems. SIAM J. Imag. Sci. 2(2), 323–343 (2009).
 Vandeghinste B., Goossens B., Holen R. V., Vanhove C., Pizurica A., Vandenberghe S., Staelens S.: Iterative CT Reconstruction Using Shearlet-Based Regularization. IEEE Trans Nuclear Science. 60(5), 3305–3317 (2013).
 Oliveira J.P., Bioucas-Dias J. M., Figueiredo M.A.T.: Adaptative total variation image deblurring: A majorization-minimization approach. Signal Process., 89, 1683–1693 (2009).
 Beck A., Teboulle M.: Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process. 18(11), 2419–2434 (2009).
 Sidky E. Y., Pan X.: Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys. Med. Biol. 53(17), 4777–4807 (2008).
 Herman G. T., Davidi R.: On image reconstruction from a small number of projections. Inv. Probl. 24(4), 45011–45028 (2008).
 Yang J., Yu H., Jiang M., Wang G.: High-order total variation minimization for interior tomography. Inv. Probl. 26(3), 035013 (2010).
 Starck JL, Candes EJ, Donoho DL.:The curvelet transform for image denoising. IEEE Trans Image Process. 11(6), 670–84 (2002).
 Wu, H., Maier, A., Hornegger, J.: Iterative CT reconstruction using curvelet-based regularization. In: Meinzer, H.-P., Deserno, T.M., Handels, H., Tolxdorff, T. (eds.) Bildverarbeitung fur die Medizin. Springer, Heidelberg (2013).
 Pour Yazdanpanah A., Regentova E. E., Bebis G.: Algebraic iterative reconstruction-reprojection (AIRR) method for high performance sparse-view CT reconstruction. Applied mathematics & information sciences. 10(6), 2007–2014 (2016).
 Pour Yazdanpanah A., Regentova E. E.: Compressed sensing MRI using curvelet sparsity and nonlocal total variation: CS-NLTV. IS&T 29th International Symposium on Electronic Imaging (2017).
 Pour Yazdanpanah A., Regentova E. E.: Sparse-View CT Reconstruction using Curvelet and TV-based Regularization. 13th International Conference Image Analysis and Recognition (ICIAR), Vol. 9730, 672–677 (2016).
 Yin, P., Lou, Y., He, Q., Xin, J.: Minimization of L1 L2 for compressed sensing. SIAM J. Sci. Comput., 37(1), A536–A563 (2014).
 Lou, Y., Yin, P., He, Q., Xin, J.: Computing sparse representation in a highly coherent dictionary based on difference of L1 and L2. J. Sci. Comput. 64(1), 178–196 (2014).
 Yifei, L., Osher, S., and Xin, J.: Computational cspects of constrained L1-L2 minimization for compressive sensing. Modelling, Computation and Optimization in Information Systems and Management Sciences, 169–180 (2015).
 R. Chartrand: Exact reconstruction of sparse signals via nonconvex minimization, IEEE Signal Process. Lett., 14, 707–710 (2007).
 R. Chartrand and V. Staneva Restricted isometry properties and nonconvex compressive sensing, Inverse Problems, 24, 1–14 (2008).
 E. Candes, M. Wakin, and S. Boyd: Enhancing sparsity by reweighted L1 minimization, J. Fourier Anal. Appl., 14, 877–905 (2008).
 E. Esser, Y. Lou, and J. Xin, A method for finding structured sparse solutions to non-negative least squares problems with applications, SIAM J. Imaging Sci., 6, 2010–2046 (2013).
 Pham-Dinh T., Le-Thi H.A.: Convex analysis approach to d.c. programming: Theory, algorithms and applications. Acta Math. Vietnam. 22(1), 289–355 (1997).
 S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Foundations and Trends in Machine Learning, 3(1), 1–122 (2011).
 Hestenes M. R., Stiefel E.: Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bureau Stand. 49(6), 409–436 (1952).
 Shepp L.A., Logan B. F.: Reconstructing interior head tissue from X-ray transmissions. IEEE Trans. Nucl. Sci. 21(1), 228–236 (1974).
 FORBILD group, http://www.imp.uni-erlangen.de/phantoms/head/head. html, Accessed on 01/10/2016.