Abstract
In this paper, a method for adaptive pure interpolation (PI) of magnetic resonance imaging (MRI) in the frequency domain, with gradient auto-regularization, is proposed. The input image is transformed into the frequency domain and convolved with the Fourier transform (FT) of a 2D sampling array (interpolation kernel) of initial LxM size. The inverse Fourier transform (IFT) is applied to the output coefficients and the edges are detected and counted. To get a denser kernel the sampling array is interpolated in the frequency domain and convolved again with the transform coefficients of the original MRI image of low resolution and transformed back into the spatial domain. The process is repeated until a maximum count of edges is reached in the output image, indicating that a local optimum magnification factor has been attained. Finally, the edges are sharpened by using an auto-regularization method. Our procedure is deterministic and independent of external information of large databases of other MRI images for obtain the high resolution output image. The proposed system improves the bi-cubic interpolation method by a mean of 3dB in peak of signal-to-noise ratio (PSNR) and until 6 dB in the best case. The structural similarity index measure (SSIM) is improved over bicubic interpolation with a mean of 0.04 and until 0.08 in the best case. It is a significant result respect to novel algorithms reported in the state of the art.
Similar content being viewed by others
References
Bloch, F. (1946). Nuclear induction. Physical Reviews, 70(7-8), 460–473.
Purcell, E., Torrey, H., Pound, R. (1946). Resonance absorption by nuclear magnetic moments in a solid. Physical Reviews, 69(1-2), 37–38.
Mayer, G., & Vrscay, E. (2007). Measuring Information Gain for Frequency- Encoded Super-resolution MRI. Magnetic Resonance Imaging, 25(7), 1058–1069.
Plenge, E., Poot, D., Bernsen, M., Kotek, G., Houston, G., Wielopolsski, P., et al. (2012). Super-resolution methods in MRI: Can they improve the trade-off between resolution, signal-to-noise ratio, and acquisition time? Magnetic Resonance in Medicine, 68(6), 1983–1993.
Tieng, Q., Cowin, G., Reutens, D., Galloway, G., Vegh, V. (2011). MRI Resolution Enhancement: How Useful are Shifted images Obtained by Changing the Demodulation requency? Magnetic Resonance in Medicine, 65(3), 664–672.
Wanga, Y., Qiao, J., Li, J., Fu, P., Chu, S., Roddick, J. (2014). Sparse representation-based MRI super-resolution reconstruction. Measurement, 47, 946–953.
Ashikawa, H., Estner, H., Herzka, D., Mcveigh, E., Halperin, H. (2014). Quantitative assessment of single-image super-resolution in myocardial scar imaging. IEEE Journal of Translation Engineering Health Medicine, 2, 1–12.
Lu, X., Huang, Z., Yuan, Y. (2015). MR image super-resolution via manifold regularized sparse learning. Neurocomputing, 162, 96–104.
Frakes, D., Dasi, L., Pekkan, K., Kitajima, H., Sundareswaran, K., Yoganathan, A., et al. (2008). A new method for registration-based medical image interpolation. IEEE Transactions on Medical Imaging, 27(3), 370–377.
Calamante, F., Tournier, J., Jackson, G., Connelly, A. (2010). Track-density imaging (TDI): Super-resolution white matter imaging using whole-brain track-density mapping. NeuroImage, 53(4), 1233–1243.
Du, B., & Zhang, L. (2011). Random-Selection-Based Anomaly detector for hyperspectral imagery. IEEE Transactions on Geoscience and Remote, 49(5), 1578–1589.
Carmi, E., Liu, S., Alon, N., Fiat, A., Fiat, D. (2006). Resolution enhancement in MRI. Magnetic Resonance Imaging, 24(2), 133–154.
Gholipour, A., Estroff, J., Warfield, S. (2010). Robust super-resolution volume reconstruction from slice acquisitions: Application to fetal brain MRI. IEEE Transactions on Medical Imaging, 29(10), 1739–1758.
Tao, D., Lin, X., Jin, L., Li, X. (2016). Principal Component 2-D Long Short-Term Memory for Font Recognition on Single Chinese characters. IEEE Transactions on Cybernetics, 46(3), 756–765.
Chen, S., Hong, X., Harris, C., Sharkey, P. (2004). Sparse modeling using orthogonal forward regression with PRESS statistic and regularization. IEEE Transactions on Systems Man and Cybernetics Part B, 34 (2), 898–911.
Tao, D., Li, X., Wu, X., Maybank, S. (2007). General tensor discriminant analysis and gabor eatures for gait recognition. IEEE Transactions on Pattern Analysis, 29(10), 1700–1715.
Zhi, R., Flierl, M., Ruan, Q., Kleijn, W. (2011). Graph-preserving sparse nonnegative matrix factorization with application to facial expression recognition. IEEE Transactions on Systems Man and Cybernetics Part B, 41 (1), 38–52.
Sun, J., Sun, J., Xu, Z., Shum, H.Y. (2011). Gradient profile prior and its applications in image Super-Resolution and enhancement. IEEE Transactions on Image Processing, 20(6), 1529–1542.
Wang, L., Xiang, S., Meng, G., Wu, H., Pan, C. (2013). Edge-Directed Single-Image Super-Resolution Via adaptive gradient magnitude Self-Interpolation. IEEE Transactions on Circuits and Systems for Video, 23(8), 1289–1299.
Leng, J., Xu, G., Zhang, Y. (2013). Medical image interpolation based on multi-resolution registration. Computers & Mathematics with Applications, 66(1), 1–18.
Zhang, K., Gao, X., Li, J., Xia, H. (2016). Single image super-resolution using regularization of non-local steering kernel regression. Signal Processing, 123, 53–63.
Gunaseelan, K., & Seethalachmi, E. (2013). Image resolution and contrast enhancement using singular value and discrete wavelet decomposition. Journal of Scientific & Industrial Research, 72(1), 31–35.
Greenspan, H. (2009). Super-resolution in medical imaging. The Computer Journal, 52(1), 43–63.
Van, E., Tham, I., Heng, C., Loo, C. (2012). Super-resolution in magnetic resonance imaging: A review. Concepts in Magnetic Resonance Part A, 40, 306–325.
Rousseau, F. (2010). A non-local approach for image super-resolution using intermodality priors. Medical Image Analysis, 14(4), 594–605.
Rousseau, F., Kim, K., Studholme, C., Koob, M., Dietemann, J. (2010). On super-resolution for fetal brain MRI. Medical Image Computing and Computer-Assisted Intervention, 6362, 355–362.
Rueda, A., Malpica, N., Romero, E. (2013). Single-image super-resolution of Brain MR images using overcomplete dictionaries. Medical Image Analysis, 17(1), 113–132.
Papoulis, A. (1966). Systems and transforms with applications in optics, 1st edn., (p. 105). New York: McGraw-Hill.
Canny, J. (1986). A computational approach to edge detection. IEEE Transactions on Pattern Analysis, 8 (6), 679–698.
Trinh, D., Luong, M., Dibos, J., Rocchisani, C. (2014). Novel example-based method for super-resolution and denoising of medical images. IEEE Transactions on Image Processing, 23(4), 1882–1895.
Ahmadi, K., & Salari, E. (2015). Edge-preserving MRI super resolution using a high frequency regularization technique. IEEE Signal Processing in Medicine and Biology Symposium (SPMB), pp. 1–5.
Zhang, Y., Liu, J., Yang, W., Guo, Z. (2015). Image super-resolution based on structure-modulated sparse representation. IEEE Transactions on Image Processing, 24(9), 2797–2810.
Sun, Y., Gu, G., Sui, X., Liu, Y. (2016). Compressive superresolution imaging based on local and nonlocal regularizations. IEEE Photonics Journal, 8(1), 1–12.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Delfin, L.M., Elias, R.P., de Jesús Ochoa Domínguez, H. et al. Auto-regularized Gradients of Adaptive Interpolation for MRI Super-Resolution. J Sign Process Syst 91, 885–898 (2019). https://doi.org/10.1007/s11265-018-1408-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11265-018-1408-1