{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:53:04Z","timestamp":1760237584570,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,6,3]],"date-time":"2020-06-03T00:00:00Z","timestamp":1591142400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Reconstruction of magnetic resonance images (MRI) benefits from incorporating a priori knowledge about statistical dependencies among the representation coefficients. Recent results demonstrate that modeling intraband dependencies with Markov Random Field (MRF) models enable superior reconstructions compared to inter-scale models. In this paper, we develop a novel reconstruction method, which includes a composite prior based on an MRF model and Total Variation (TV). We use an anisotropic MRF model and propose an original data-driven method for the adaptive estimation of its parameters. From a Bayesian perspective, we define a new position-dependent type of regularization and derive a compact reconstruction algorithm with a novel soft-thresholding rule. Experimental results show the effectiveness of this method compared to the state of the art in the field.<\/jats:p>","DOI":"10.3390\/s20113185","type":"journal-article","created":{"date-parts":[[2020,6,4]],"date-time":"2020-06-04T04:36:09Z","timestamp":1591245369000},"page":"3185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["MRI Reconstruction Using Markov Random Field and Total Variation as Composite Prior"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7993-6826","authenticated-orcid":false,"given":"Marko","family":"Pani\u0107","sequence":"first","affiliation":[{"name":"BioSense Institute, University of Novi Sad, 21000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Du\u0161an","family":"Jakoveti\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Sciences, University of Novi Sad, 21000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dejan","family":"Vukobratovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, 21000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladimir","family":"Crnojevi\u0107","sequence":"additional","affiliation":[{"name":"BioSense Institute, University of Novi Sad, 21000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9322-4999","authenticated-orcid":false,"given":"Aleksandra","family":"Pi\u017eurica","sequence":"additional","affiliation":[{"name":"Department of Telecommunications and Information Processing, Ghent University, 9000 Ghent, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Deka, B., and Datta, S. (2019). Compressed Sensing Magnetic Resonance Image Reconstruction Algorithms, Springer.","DOI":"10.1007\/978-981-13-3597-6"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1109\/MSP.2019.2943645","article-title":"Optimization methods for magnetic resonance image reconstruction: Key models and optimization algorithms","volume":"37","author":"Fessler","year":"2020","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1109\/MSP.2019.2949470","article-title":"Plug-and-Play Methods for Magnetic Resonance Imaging: Using Denoisers for Image Recovery","volume":"37","author":"Ahmad","year":"2020","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1002\/mrm.21391","article-title":"Sparse MRI: The application of compressed sensing for rapid MR imaging","volume":"58","author":"Lustig","year":"2007","journal-title":"Magn. Reson. Med."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1016\/j.media.2011.06.001","article-title":"Efficient MR image reconstruction for compressed MR imaging","volume":"15","author":"Huang","year":"2011","journal-title":"Med. Image Anal."},{"key":"ref_6","unstructured":"Ma, S., Yin, W., Zhang, Y., and Chakraborty, A. (2008, January 23\u201328). An efficient algorithm for compressed MR imaging using total variation and wavelets. Proceedings of the 2008 IEEE Conference on Computer Vision and Pattern Recognition, Anchorage, AK, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1109\/JSTSP.2010.2042333","article-title":"A fast alternating direction method for TV\u21131-\u21132 signal reconstruction from partial Fourier data","volume":"4","author":"Yang","year":"2010","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1109\/TMI.2016.2553401","article-title":"Guest editorial deep learning in medical imaging: Overview and future promise of an exciting new technique","volume":"35","author":"Greenspan","year":"2016","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TMI.2018.2833635","article-title":"Image reconstruction is a new frontier of machine learning","volume":"37","author":"Wang","year":"2018","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1137\/17M1141771","article-title":"Deep convolutional framelets: A general deep learning framework for inverse problems","volume":"11","author":"Ye","year":"2018","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, S., Su, Z., Ying, L., Peng, X., Zhu, S., Liang, F., Feng, D., and Liang, D. (2016, January 13\u201316). Accelerating magnetic resonance imaging via deep learning. Proceedings of the 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), Prague, Czech Republic.","DOI":"10.1109\/ISBI.2016.7493320"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"135007","DOI":"10.1088\/1361-6560\/aac71a","article-title":"Deep learning for undersampled MRI reconstruction","volume":"63","author":"Hyun","year":"2018","journal-title":"Phys. Med. Biol."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015). U-net: Convolutional networks for biomedical image segmentation. International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1109\/TMI.2019.2927101","article-title":"k-space deep learning for accelerated MRI","volume":"39","author":"Han","year":"2019","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1310","DOI":"10.1109\/TMI.2017.2785879","article-title":"DAGAN: Deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction","volume":"37","author":"Yang","year":"2017","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_16","unstructured":"Yu, S., Dong, H., Yang, G., Slabaugh, G., Dragotti, P.L., Ye, X., Liu, F., Arridge, S., Keegan, J., and Firmin, D. (2017). Deep de-aliasing for fast compressive sensing mri. arXiv."},{"key":"ref_17","unstructured":"Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. (2014, January 8\u201313). Generative adversarial nets. Proceedings of the Twenty-Eighth Conference on Neural Information Processing Systems, Montreal, QC, Canada."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/TMI.2017.2760978","article-title":"A deep cascade of convolutional neural networks for dynamic MR image reconstruction","volume":"37","author":"Schlemper","year":"2017","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Schlemper, J., Yang, G., Ferreira, P., Scott, A., McGill, L.A., Khalique, Z., Gorodezky, M., Roehl, M., Keegan, J., and Pennell, D. (2018). Stochastic deep compressive sensing for the reconstruction of diffusion tensor cardiac MRI. International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer.","DOI":"10.1007\/978-3-030-00928-1_34"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, C., Papanastasiou, G., Tsaftaris, S., Yang, G., Gray, C., Newby, D., Macnaught, G., and MacGillivray, T. (2019). TPSDicyc: Improved Deformation Invariant Cross-domain Medical Image Synthesis. International Workshop on Machine Learning for Medical Image Reconstruction, Springer.","DOI":"10.1007\/978-3-030-33843-5_23"},{"key":"ref_21","unstructured":"Zhu, J., Yang, G., Ferreira, P., Scott, A., Nielles-Vallespin, S., Keegan, J., Pennell, D., Lio, P., and Firmin, D. (2019, January 11\u201316). A ROI Focused Multi-Scale Super-Resolution Method for the Diffusion Tensor Cardiac Magnetic Resonance. Proceedings of the 27th Annual Meeting (ISMRM), Montr\u00e9al, QC, Canada."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhu, J., Yang, G., and Lio, P. (2019, January 8\u201311). How can we make gan perform better in single medical image super-resolution? A lesion focused multi-scale approach. Proceedings of the 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019), Venice, Italy.","DOI":"10.1109\/ISBI.2019.8759517"},{"key":"ref_23","first-page":"109491L","article-title":"Lesion focused super-resolution","volume":"Volume 10949","author":"Zhu","year":"2019","journal-title":"Medical Imaging 2019: Image Processing"},{"key":"ref_24","unstructured":"Chen, C., and Huang, J. (2012, January 3\u20138). Compressive sensing MRI with wavelet tree sparsity. Proceedings of the Twenty-Sixth Annual Conference on Neural Information Processing Systems, Lake Tahoe, NV, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1016\/j.mri.2014.07.016","article-title":"Exploiting the wavelet structure in compressed sensing MRI","volume":"32","author":"Chen","year":"2014","journal-title":"Magn. Reson. Imaging"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Cevher, V., Duarte, M.F., Hegde, C., and Baraniuk, R. (2009, January 7\u201310). Sparse signal recovery using Markov random fields. Proceedings of the 23rd Annual Conference on Neural Information Processing Systems, Vancouver, BC, Canada.","DOI":"10.21236\/ADA520187"},{"key":"ref_27","first-page":"333","article-title":"On structured sparsity and selected applications in tomographic imaging","volume":"Volume 8138","author":"Aelterman","year":"2011","journal-title":"SPIE Conference on Wavelets and Sparsity XIV"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Pani\u0107, M., Aelterman, J., Crnojevi\u0107, V., and Pi\u017eurica, A. (2, January 29). Compressed Sensing in MRI with a Markov Random Field prior for spatial clustering of subband coefficients. Proceedings of the 24th European Signal Processing Conference, EUSIPCO 2016, Budapest, Hungary.","DOI":"10.1109\/EUSIPCO.2016.7760311"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2104","DOI":"10.1109\/TMI.2017.2743819","article-title":"Sparse Recovery in Magnetic Resonance Imaging With a Markov Random Field Prior","volume":"36","author":"Aelterman","year":"2017","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1109\/TIP.2010.2076294","article-title":"An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems","volume":"20","author":"Afonso","year":"2011","journal-title":"IEEE Trans. Image Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2130","DOI":"10.1109\/TMI.2016.2550080","article-title":"Projected iterative soft-thresholding algorithm for tight frames in compressed sensing magnetic resonance imaging","volume":"35","author":"Liu","year":"2016","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1109\/TMI.2010.2090538","article-title":"MR image reconstruction from highly undersampled k-space data by dictionary learning","volume":"30","author":"Ravishankar","year":"2011","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_33","first-page":"543","article-title":"A method of solving a convex programming problem with convergence rate O( k^2)","volume":"Volume 269","author":"Nesterov","year":"1983","journal-title":"Doklady Akademii Nauk"},{"key":"ref_34","unstructured":"Nesterov, Y. (2013). Introductory Lectures on Convex Optimization: A Basic Course, Springer Science & Business Media."},{"key":"ref_35","first-page":"92","article-title":"Sparse signal recovery and acquisition with graphical models","volume":"27","author":"Cevher","year":"2010","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_36","unstructured":"Li, S.Z. (2009). Markov Random Field Modeling in Image Analysis, Springer Science & Business Media."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1610","DOI":"10.1016\/j.cviu.2011.06.011","article-title":"Composite splitting algorithms for convex optimization","volume":"115","author":"Huang","year":"2011","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1002\/mrm.26182","article-title":"LORAKS makes better SENSE: Phase-constrained partial fourier SENSE reconstruction without phase calibration","volume":"77","author":"Kim","year":"2017","journal-title":"Magn. Reson. Med."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Huang, J., and Yang, F. (2012, January 2\u20135). Compressed magnetic resonance imaging based on wavelet sparsity and nonlocal total variation. Proceedings of the 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), Barcelona, Spain.","DOI":"10.1109\/ISBI.2012.6235718"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1002\/mrm.25717","article-title":"P-LORAKS: Low-rank modeling of local k-space neighborhoods with parallel imaging data","volume":"75","author":"Haldar","year":"2016","journal-title":"Magn. Reson. Med."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/TMI.2006.885337","article-title":"An optimal radial profile order based on the Golden Ratio for time-resolved MRI","volume":"26","author":"Winkelmann","year":"2007","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Seitzer, M., Yang, G., Schlemper, J., Oktay, O., W\u00fcrfl, T., Christlein, V., Wong, T., Mohiaddin, R., Firmin, D., and Keegan, J. (2018). Adversarial and perceptual refinement for compressed sensing MRI reconstruction. International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer.","DOI":"10.1007\/978-3-030-00928-1_27"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/11\/3185\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:35:28Z","timestamp":1760175328000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/11\/3185"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,3]]},"references-count":42,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["s20113185"],"URL":"https:\/\/doi.org\/10.3390\/s20113185","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,6,3]]}}}