Abstract
A major challenge in contemporary magnetic resonance imaging (MRI) lies in providing the highest resolution exam possible in the shortest acquisition period. Recently, several authors have proposed the use of L1-norm minimization for the reconstruction of sparse MR images from highly-undersampled k-space data. Despite promising results demonstrating the ability to accurately reconstruct images sampled at rates significantly below the Nyquist criterion, the extensive computational complexity associated with the existing framework limits its clinical practicality. In this work, we propose an alternative recovery framework based on homotopic approximation of the L0-norm and extend the reconstruction problem to a multiscale formulation. In addition to several interesting theoretical properties, practical implementation of this technique effectively resorts to a simple iterative alternation between bilteral filtering and projection of the measured k-space sample set that can be computed in a matter of seconds on a standard PC.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Noll, D., Nishimura, D., Macovski, A.: Homodyne detection in magnetic resonance imaging. IEEE Trans. Med. Imag. 10(2), 154–163 (1991)
Haacke, E., Lindskog, E., Lin, W.: A fast, iterative, partial-fourier technique capable of local phase recovery. J. Mag. Res. 92, 125–146 (1991)
Lustig, M., Donoho, D., Pauly, J.: Sparse MRI: the application of compressed sensing for rapid MR imaging. Manuscript (2007)
He, L., Chang, T., Osher, S., Fang, T., Speier, P.: MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods. UCLA CAM Reports 06-35 (2006)
Boubertakh, R., Giovanelli, J., Cesare, A.D., Herment, A.: Non-quadratic convex regularized reconstruction of MR images from spiral acquisitions. Sig. Proc. 86, 2479–2494 (2006)
Chartrand, R.: Exact reconstruction of sparse signal via nonconvex minimization. Manuscript (2007)
Kim, S., Koh, K., Lustig, M., Boyd, S., Gorinevsky, D.: A method for large-scale l1-regularized least squares problems with applications in signal processing and statistics. Manuscript (2007)
Black, M., Sapiro, G., Marimon, D., Heeger, D.: Robust anisotropic diffusion. IEEE Trans. Imag. Proc. 7(3), 421–432 (1998)
Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proc. IEEE ICIP (1998)
Takeda, H., Farsiu, S., Milanfar, P.: Kernel regression for image processing and reconstruction. IEEE Trans. Imag. Proc. 16(2), 349–366 (2007)
Candés, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Info. Theory 52(2), 489–509 (2006)
Donoho, D.: Compressed sensing. IEEE Trans. Info. Theory 52(4), 1289–1306 (2006)
Candés, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59, 1207–1223 (2006)
Chen, S., Donoho, D., Saunders, M.: Atomic decomposition by basis pursuit. SIAM J. Sci. Comp. 20(1), 33–61 (1998)
Chan, T., Zhou, H., Chan, R.: Continuation method for total variation denoising. UCLA CAM Reports 95-28 (1995)
Huber, P.: Robust Statistics. Wiley, New York (1981)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Patt. Anal. Mach. Intel. 12(7), 629–639 (1990)
Geman, D., Reynolds, G.: Constrained restoration and the recovery of discontinuities. IEEE Trans. Patt. Anal. Mach. Intel. 14(3), 367–383 (1990)
Pham, T., van Vliet, L.: Separable bilateral filtering for fast video preprocessing. In: Proc. IEEE ICME (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Trzasko, J., Manduca, A., Borisch, E. (2007). Robust Kernel Methods for Sparse MR Image Reconstruction. In: Ayache, N., Ourselin, S., Maeder, A. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007. MICCAI 2007. Lecture Notes in Computer Science, vol 4791. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75757-3_98
Download citation
DOI: https://doi.org/10.1007/978-3-540-75757-3_98
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75756-6
Online ISBN: 978-3-540-75757-3
eBook Packages: Computer ScienceComputer Science (R0)