Fast 3D Volume Super Resolution Using an Analytical Solution for l2-l2 Problems

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Rose Sfeir 1,* Bilal Chebaro 1 Charbel Julien 1

1. Computer Science Department, Lebanese University, Hadath, Lebanon

* Corresponding author.


Received: 4 Feb. 2020 / Revised: 19 Feb. 2020 / Accepted: 15 Mar. 2020 / Published: 8 Aug. 2020

Index Terms

Super Resolution, Inverse Problems, CBCT, MCT, Endodontics.


In Endodontics, dentists need a good visualization of dental root canals as found in Cone Beam Computed Tomography (CBCT) dental volumes to diagnose and prevent the development of some anomalies. These CBCT dental volumes, however, suffer from low resolution. In order, to enhance their resolution, we need to apply a super-resolution technique. In this paper, we propose a new 3D super resolution algorithm based on a linear model, consisting of a blurring operator and a decimation operator, which is an extension of Zhao’s work [1] in 3D, taking the low-resolution volume as an input and producing the high-resolution volume as an output. We present a generalization of the 2D Super-Resolution problem into a 3D Super- Resolution problem as we apply it to 3D dental volume. Our new Super-Resolution algorithm as applied to dental CBCT volumes is a direct method aiming to get the exact solution with a short computation time. Results show an improvement in the resolution of the CBCT in a short time in comparison with Zhao’s work, which was applied to CBCT dental volumes slice by slice, [2].

Cite This Paper

Rose Sfeir, Bilal Chebaro, Charbel Julien, " Fast 3D Volume Super Resolution Using an Analytical Solution for l2-l2 Problems", International Journal of Image, Graphics and Signal Processing(IJIGSP), Vol.12, No.4, pp. 29-46, 2020. DOI: 10.5815/ijigsp.2020.04.03


[1]Zhao, N., Wei, Q., Basarab, A., Dobigeon, N., Kouamé, D., Tourneret J.-Y., Fast, J.-Y., Member, Student, Member, Senior, 2016. Fast Single Image Super-Resolution Using a New Analytical Solution for l2–l2 Problems. IEEE Trans. Image Process. 25, 3683–3697.ï

[2]Sfeir, R., Michetti, J., Chebaro, B., Diemer, F., Basarab, A., Kouame, D., 2018. Dental root canal segmentation from super-resolved 3D cone beam computed tomography data, in: 2017 IEEE Nuclear Science Symposium and Medical Imaging Conference, NSS/MIC 2017 – Conference Proceedings. pp. 1–2.

[3]Yang, J., Huang, T., 2010. Image super-resolution: Historical overview and future challenges.

[4]Tai, Y.W., Liu, S., Brown, M.S., Lin, S., 2010. Super resolution using edge prior and single image detail synthesis, in: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[5]Blu, T., Blu, T., Unser, M., 2000. Image Interpolation and Resampling. Handb. Med. IMAGING, Process. Anal. 393–420. 

[6]Zhang, X., Wu, X., 2008. Image interpolation by adaptive 2-D autoregressive modeling and soft-decision estimation. IEEE Trans. Image Process.

[7]Mallat, S., Yu, G., 2010. Super-resolution with sparse mixing estimators. IEEE Trans. Image Process.

[8]Freeman, W.T., Pasztor, E.C., Carmichael, O.T., 2000. Learning low-level vision. Int. J. Comput. Vis.

[9]Zeyde, R., Elad, M., Protter, M., 2012. On single image scale-up using sparse-representations, in: Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).

[10]Dong, C., Loy, C.C., He, K., Tang, X., 2014. Learning a deep convolutional network for image super-resolution, in: Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).

[11]Yang, C.-Y., Ma, C., Yang, M.-H., 2014. Single-Image Super-Resolution: A Benchmark. Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics).

[12]Ng, M.K., Weiss, P., Yuan, X., 2010. Solving Constrained Total-variation Image Restoration and Reconstruction Problems via Alternating Direction Methods. SIAM J. Sci. Comput.

[13]Sun, J., Xu, Z., Shum, H.-Y., 2008. Image Super-Resolution using Gradient Profile Prior. 26th IEEE Conf. Comput. Vis. Pattern Recognition, CVPR.

[14]Sun, J., Xu, Z., Shum, H.Y., 2011. Gradient profile prior and its applications in image super-resolution and enhancement. IEEE Trans. Image Process.

[15]Beck, A., Teboulle, M., 2009. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183–202.

[16]Martín, G., On, J.B.-D., 2015. Hyperspectral compressive acquisition in the spatial domain via blind factorization. 7th Worksh.

[17]Morin, R., Basarab, A., Kouamé, D., 2012. Alternating Direction Method of Multipliers Framework for Super-Resolution in Ultrasound Imaging. Proc. - Int. Symp. Biomed. Imaging.

[18]Marquina, A., Osher, S., Osher, S.J., 2008. Image Super-Resolution by TV-Regularization and Bregman Iteration Signal and Image Processing : applications to Laser interferometry and Magnetic resonance spectroscopy View project Non-local Retinex View project Image Super-Resolution by TV-Regularization. J. Sci. Comput. 37, 367–382.

[19]Shi, F., Cheng, J., Wang, L. P.Y.-I. transactions on, 2015, U., 2015. LRTV: MR image super-resolution with low-rank and total variation regularizations.

[20]Elad, M., Processing, A.F.-I. transactions on image, 1997, U., 1997. Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images.

[21]Farsiu, S., Robinson, D., Elad, M., Milanfar, P., 2004. Advances and Challenges in Super-Resolution. Int J Imaging Syst Technol 14, 47–57.

[22]Glazistov, I., Petrova, X., 2018. Superfast joint demosaicing and super-resolution. Electron. Imaging.

[23]Wei, Q., Dobigeon, N., Tourneret, J.Y., 2015. Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation. IEEE Trans. Image Process.

[24]Eberhard, A., 2012. Transformée de Fourier Discrète Course, Vol. 87, 2004.