Abstract
We propose a novel image resolution enhancement method for multidimensional images based on a variational approach. Given an appropriate down-sampling operator, the reconstruction problem is posed using a deconvolution model under the assumption of Gaussian noise. In order to preserve edges in the image, we regularize the optimization problem by the norm of the total variation of the image. Additionally, we propose a new edge-preserving operator that emphasizes and even enhances edges during the up-sampling and decimation of the image. Furthermore, we also propose the use of the Bregman iterative refinement procedure for the recovery of higher order information from the image. This is coarse to fine approach for recovering finer scales in the image first, followed by the noise. This method is demonstrated on a variety of low-resolution, natural images as well as 3D anisotropic brain MRI images. The edge enhanced reconstruction is shown to yield significant improvement in resolution, especially preserving important edges containing anatomical information.
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References
Bregman, L.M.: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. and Math. Phys. 7, 200–217 (1967)
Capel, D., Zisserman, A.: Super-resolution from multiple views using learnt image models. In: CVPR, vol. 2, pp. 627–634 (2001)
Carmi, E., Liu, S., Alon, N., Fiat, A., Fiat, D.: Resolution enhancement in MRI. Magnetic Resonance Imaging 24(2), 133–154 (2006)
Chaudhuri, S., Joshi, M.: Motion-Free Super-Resolution. Springer, New York (2005)
Elad, M., Feuer, A.: Restoration of a single super-resolution image from several blurred,noisy, and undersampled measured images. IEEE Tran. Image Processing 6(12), 1646–1658 (1997)
Freeman, W.T., Jones, T.R., Pasztor, E.C.: Example-based super-resolution. IEEE Computer Graphics and Applications 22(2), 56–65 (2002)
Greenspan, H., Oz, G., Kiryati, N., Peled, S.: MRI inter-slice reconstruction. Magnetic Resonance Imaging 20, 437–446 (2002)
Irani, M., Peleg, S.: Improving resolution by image registration. CVGIP: Graphical Models and Image Processing 53(3), 231–239 (1991)
Kornprobst, P., Peeters, R., Nikolova, M., Deriche, R., Ng, M., Van Hecke, P.: A superresolution framework for fMRI sequences and its impact on resulting activation maps. In: Ellis, R.E., Peters, T.M. (eds.) MICCAI 2003. LNCS, vol. 2879, pp. 117–125. Springer, Heidelberg (2003)
Osher, S.J., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterative regularization method for Total Variation-based image restoration. Multiscale Modeling and Simulation 4(2), 460–489 (2005)
Rudin, L.I., Osher, S.J., Fatemi, E.: Nonlinear Total Variation based noise removal algorithms. Physica D 60(1-4), 259–268 (1992)
Startk, H., Oskoui, P.: High-resolution image recovery from image-plane arrays, using convex projections. Journal of the Optical Society of America 6, 1715–1726 (1989)
Tsai, R.Y., Huang, T.S.: Multi-frame image restoration and registration. In: Advances in Computer Vision and Image Processing, pp. 317–339 (1984)
Marquina, A., Osher, S.J.: Image super-resolution by TV-regularization and Bregman iteration. Journal of Scientific Computing 37(3), 367–382 (2008)
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Joshi, S.H., Marquina, A., Osher, S.J., Dinov, I., Van Horn, J.D., Toga, A.W. (2009). Edge-Enhanced Image Reconstruction Using (TV) Total Variation and Bregman Refinement. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_33
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DOI: https://doi.org/10.1007/978-3-642-02256-2_33
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