{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:51:20Z","timestamp":1761709880252,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,7,4]],"date-time":"2021-07-04T00:00:00Z","timestamp":1625356800000},"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>To create a realistic 3D perception on glasses-free displays, it is critical to support continuous motion parallax, greater depths of field, and wider fields of view. A new type of Layered or Tensor light field 3D display has attracted greater attention these days. Using only a few light-attenuating pixelized layers (e.g., LCD panels), it supports many views from different viewing directions that can be displayed simultaneously with a high resolution. This paper presents a novel flexible scheme for efficient layer-based representation and lossy compression of light fields on layered displays. The proposed scheme learns stacked multiplicative layers optimized using a convolutional neural network (CNN). The intrinsic redundancy in light field data is efficiently removed by analyzing the hidden low-rank structure of multiplicative layers on a Krylov subspace. Factorization derived from Block Krylov singular value decomposition (BK-SVD) exploits the spatial correlation in layer patterns for multiplicative layers with varying low ranks. Further, encoding with HEVC eliminates inter-frame and intra-frame redundancies in the low-rank approximated representation of layers and improves the compression efficiency. The scheme is flexible to realize multiple bitrates at the decoder by adjusting the ranks of BK-SVD representation and HEVC quantization. Thus, it would complement the generality and flexibility of a data-driven CNN-based method for coding with multiple bitrates within a single training framework for practical display applications. Extensive experiments demonstrate that the proposed coding scheme achieves substantial bitrate savings compared with pseudo-sequence-based light field compression approaches and state-of-the-art JPEG and HEVC coders.<\/jats:p>","DOI":"10.3390\/s21134574","type":"journal-article","created":{"date-parts":[[2021,7,4]],"date-time":"2021-07-04T22:35:22Z","timestamp":1625438122000},"page":"4574","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Flexible Coding Scheme Based on Block Krylov Subspace Approximation for Light Field Displays with Stacked Multiplicative Layers"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8252-1827","authenticated-orcid":false,"given":"Joshitha","family":"Ravishankar","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3243-3321","authenticated-orcid":false,"given":"Mansi","family":"Sharma","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8238-6776","authenticated-orcid":false,"given":"Pradeep","family":"Gopalakrishnan","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,4]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Surman, P., and Sun, X.W. (2014, January 2\u20134). Towards the reality of 3D imaging and display. Proceedings of the 2014 3DTV-Conference: The True Vision-Capture, Transmission and Display of 3D Video (3DTV-CON), Budapest, Hungary.","key":"ref_1","DOI":"10.1109\/3DTV.2014.6874764"},{"doi-asserted-by":"crossref","unstructured":"Li, T., Huang, Q., Alfaro, S., Supikov, A., Ratcliff, J., Grover, G., and Azuma, R. (2020, January 17\u201328). Light-Field Displays: A View-Dependent Approach. Proceedings of the ACM SIGGRAPH 2020 Emerging Technologies, Online.","key":"ref_2","DOI":"10.1145\/3388534.3407293"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"17688","DOI":"10.1038\/s41598-019-54243-6","article-title":"Aktina Vision: Full-parallax three-dimensional display with 100 million light rays","volume":"9","author":"Watanabe","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1364\/AOP.5.000456","article-title":"Three-dimensional display technologies","volume":"5","author":"Geng","year":"2013","journal-title":"Adv. Opt. Photonics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1145\/2185520.2185576","article-title":"Tensor Displays: Compressive Light Field Synthesis Using Multilayer Displays with Directional Backlighting","volume":"31","author":"Wetzstein","year":"2012","journal-title":"ACM Trans. Graph."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2098","DOI":"10.1109\/TCSVT.2016.2564798","article-title":"A novel hybrid kinect-variety-based high-quality multiview rendering scheme for glass-free 3D displays","volume":"27","author":"Sharma","year":"2016","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1016\/j.jvcir.2013.07.012","article-title":"A flexible architecture for multi-view 3DTV based on uncalibrated cameras","volume":"25","author":"Sharma","year":"2014","journal-title":"J. Vis. Commun. Image Represent."},{"unstructured":"Sharma, M. (2017). Uncalibrated Camera Based Content Generation for 3D Multi-View Displays. [Ph.D. Thesis, Indian Institute of Technology Delhi].","key":"ref_8"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2601097.2601144","article-title":"A compressive light field projection system","volume":"33","author":"Hirsch","year":"2014","journal-title":"ACM Trans. Graph."},{"doi-asserted-by":"crossref","unstructured":"Balogh, T., Kov\u00e1cs, P.T., and Barsi, A. (2007, January 7\u20139). Holovizio 3D display system. Proceedings of the 2007 3DTV Conference, Kos, Greece.","key":"ref_10","DOI":"10.1109\/3DTV.2007.4379386"},{"doi-asserted-by":"crossref","unstructured":"Takahashi, K., Saito, T., Tehrani, M.P., and Fujii, T. (2015, January 27\u201330). Rank analysis of a light field for dual-layer 3D displays. Proceedings of the 2015 IEEE International Conference on Image Processing (ICIP), Quebec City, QC, Canada.","key":"ref_11","DOI":"10.1109\/ICIP.2015.7351685"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1109\/JDT.2016.2594804","article-title":"Displaying real-world light fields with stacked multiplicative layers: Requirement and data conversion for input multiview images","volume":"12","author":"Saito","year":"2016","journal-title":"J. Disp. Technol."},{"doi-asserted-by":"crossref","unstructured":"Kobayashi, Y., Takahashi, K., and Fujii, T. (2017, January 5\u20139). From focal stacks to tensor display: A method for light field visualization without multi-view images. Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA.","key":"ref_13","DOI":"10.1109\/ICASSP.2017.7952508"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"38767","DOI":"10.1109\/ACCESS.2020.2975209","article-title":"Comparison of Layer Operations and Optimization Methods for Light Field Display","volume":"8","author":"Maruyama","year":"2020","journal-title":"IEEE Access"},{"key":"ref_15","first-page":"88","article-title":"A 3-D display pipeline: Capture, factorize, and display the light field of a real 3-D scene","volume":"5","author":"Kobayashi","year":"2017","journal-title":"ITE Trans. Media Technol. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4571","DOI":"10.1109\/TIP.2018.2839263","article-title":"From focal stack to tensor light-field display","volume":"27","author":"Takahashi","year":"2018","journal-title":"IEEE Trans. Image Process."},{"doi-asserted-by":"crossref","unstructured":"Maruyama, K., Inagaki, Y., Takahashi, K., Fujii, T., and Nagahara, H. (2019, January 22\u201325). A 3-D display pipeline from coded-aperture camera to tensor light-field display through CNN. Proceedings of the 2019 IEEE International Conference on Image Processing (ICIP), Taipei, Taiwan.","key":"ref_17","DOI":"10.1109\/ICIP.2019.8803741"},{"key":"ref_18","first-page":"1","article-title":"Additive light field displays: Realization of augmented reality with holographic optical elements","volume":"35","author":"Lee","year":"2016","journal-title":"ACM Trans. Graph."},{"doi-asserted-by":"crossref","unstructured":"Thumuluri, V., and Sharma, M. (2020, January 15). A Unified Deep Learning Approach for Foveated Rendering & Novel View Synthesis from Sparse RGB-D Light Fields. Proceedings of the 2020 International Conference on 3D Immersion (IC3D 2020), Brussels, Belgium.","key":"ref_19","DOI":"10.1109\/IC3D51119.2020.9376340"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2661229.2661260","article-title":"Cascaded displays: Spatiotemporal superresolution using offset pixel layers","volume":"33","author":"Heide","year":"2014","journal-title":"ACM Trans. Graph."},{"key":"ref_21","first-page":"60","article-title":"The Light Field Stereoscope: Immersive Computer Graphics via Factored Near-Eye Light Field Displays with Focus Cues","volume":"34","author":"Hung","year":"2015","journal-title":"ACM Trans. Graph."},{"unstructured":"Maruyama, K., Kojima, H., Takahashi, K., and Fujii, T. (2018, January 12\u201314). Implementation of Table-Top Light-Field Display. Proceedings of the International Display Workshops (IDW 2018), Nagoya, Japan.","key":"ref_22"},{"doi-asserted-by":"crossref","unstructured":"Liu, D., Wang, L., Li, L., Xiong, Z., Wu, F., and Zeng, W. (2016, January 11\u201315). Pseudo-sequence-based light field image compression. Proceedings of the 2016 IEEE International Conference on Multimedia & Expo Workshops (ICMEW), Seattle, WA, USA.","key":"ref_23","DOI":"10.1109\/ICMEW.2016.7574674"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1109\/JSTSP.2017.2725198","article-title":"Pseudo-sequence-based 2-D hierarchical coding structure for light-field image compression","volume":"11","author":"Li","year":"2017","journal-title":"IEEE J. Sel. Top. Signal Process."},{"doi-asserted-by":"crossref","unstructured":"Ahmad, W., Olsson, R., and Sj\u00f6str\u00f6m, M. (2017, January 17\u201320). Interpreting plenoptic images as multi-view sequences for improved compression. Proceedings of the 2017 IEEE International Conference on Image Processing (ICIP), Beijing, China.","key":"ref_25","DOI":"10.1109\/ICIP.2017.8297145"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"143002","DOI":"10.1109\/ACCESS.2019.2944765","article-title":"Computationally efficient light field image compression using a multiview HEVC framework","volume":"7","author":"Ahmad","year":"2019","journal-title":"IEEE Access"},{"doi-asserted-by":"crossref","unstructured":"Gu, J., Guo, B., and Wen, J. (2019, January 8\u201312). High efficiency light field compression via virtual reference and hierarchical MV-HEVC. Proceedings of the 2019 IEEE International Conference on Multimedia and Expo (ICME), Shanghai, China.","key":"ref_27","DOI":"10.1109\/ICME.2019.00067"},{"doi-asserted-by":"crossref","unstructured":"Sharma, M., and Ragavan, G. (2019, January 11). A Novel Randomize Hierarchical Extension of MV-HEVC for Improved Light Field Compression. Proceedings of the 2019 International Conference on 3D Immersion (IC3D), Brussels, Belgium.","key":"ref_28","DOI":"10.1109\/IC3D48390.2019.8975905"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1109\/TCSVT.2012.2221191","article-title":"Overview of the high efficiency video coding (HEVC) standard","volume":"22","author":"Sullivan","year":"2012","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"doi-asserted-by":"crossref","unstructured":"Senoh, T., Yamamoto, K., Tetsutani, N., and Yasuda, H. (2018, January 3\u20137). Efficient light field image coding with depth estimation and view synthesis. Proceedings of the 2018 26th European Signal Processing Conference (EUSIPCO), Rome, Italy.","key":"ref_30","DOI":"10.23919\/EUSIPCO.2018.8553373"},{"doi-asserted-by":"crossref","unstructured":"Huang, X., An, P., Shan, L., Ma, R., and Shen, L. (2018, January 23\u201327). View synthesis for light field coding using depth estimation. Proceedings of the 2018 IEEE International Conference on Multimedia and Expo (ICME), San Diego, CA, USA.","key":"ref_31","DOI":"10.1109\/ICME.2018.8486515"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3557","DOI":"10.1364\/OE.27.003557","article-title":"Light-field compression using a pair of steps and depth estimation","volume":"27","author":"Huang","year":"2019","journal-title":"Opt. Express"},{"doi-asserted-by":"crossref","unstructured":"H\u00e9riard-Dubreuil, B., Viola, I., and Ebrahimi, T. (2019, January 12\u201315). Light field compression using translation-assisted view estimation. Proceedings of the 2019 Picture Coding Symposium (PCS), Ningbo, China.","key":"ref_33","DOI":"10.1109\/PCS48520.2019.8954495"},{"doi-asserted-by":"crossref","unstructured":"Bakir, N., Hamidouche, W., D\u00e9forges, O., Samrouth, K., and Khalil, M. (2018, January 7\u201310). Light field image compression based on convolutional neural networks and linear approximation. Proceedings of the 2018 25th IEEE International Conference on Image Processing (ICIP), Athens, Greece.","key":"ref_34","DOI":"10.1109\/ICIP.2018.8451597"},{"doi-asserted-by":"crossref","unstructured":"Zhao, Z., Wang, S., Jia, C., Zhang, X., Ma, S., and Yang, J. (2018, January 23\u201327). Light field image compression based on deep learning. Proceedings of the 2018 IEEE International Conference on Multimedia and Expo (ICME), San Diego, CA, USA.","key":"ref_35","DOI":"10.1109\/ICME.2018.8486546"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"41183","DOI":"10.1109\/ACCESS.2019.2907572","article-title":"Region-of-interest compression and view synthesis for light field video streaming","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"unstructured":"Schiopu, I., and Munteanu, A. (2019). Deep-Learning-Based Macro-Pixel Synthesis and Lossless Coding of Light Field Images, APSIPA Transactions on Signal and Information Processing; Cambridge University Press. Available online: https:\/\/www.cambridge.org\/core\/journals\/apsipa-transactions-on-signal-and-information-processing\/article\/deeplearningbased-macropixel-synthesis-and-lossless-coding-of-light-field-images\/42FD961A4566AB4609604204B6B517CD.","key":"ref_37"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1109\/JETCAS.2018.2886642","article-title":"Light field image compression using generative adversarial network-based view synthesis","volume":"9","author":"Jia","year":"2018","journal-title":"IEEE J. Emerg. Sel. Top. Circuits Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.ins.2020.07.073","article-title":"View synthesis-based light field image compression using a generative adversarial network","volume":"545","author":"Liu","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1109\/JSTSP.2017.2747078","article-title":"Light field compression with homography-based low-rank approximation","volume":"11","author":"Jiang","year":"2017","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"9641","DOI":"10.1109\/TIP.2020.3029655","article-title":"Local low rank approximation with a parametric disparity model for light field compression","volume":"29","author":"Dib","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1109\/TPAMI.2017.2653101","article-title":"Light field reconstruction using shearlet transform","volume":"40","author":"Vagharshakyan","year":"2017","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4269","DOI":"10.1109\/TIP.2020.2969087","article-title":"Shearlet transform-based light field compression under low bitrates","volume":"29","author":"Ahmad","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1109\/LSP.2020.3003533","article-title":"Light Field Compression Using Global Multiplane Representation and Two-Step Prediction","volume":"27","author":"Chen","year":"2020","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1109\/TMM.2019.2934426","article-title":"Content-based light field image compression method with Gaussian process regression","volume":"22","author":"Liu","year":"2019","journal-title":"IEEE Trans. Multimed."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3422360","article-title":"An adaptive two-layer light field compression scheme using GNN-based reconstruction","volume":"16","author":"Hu","year":"2020","journal-title":"Acm Trans. Multimed. Comput. Commun. Appl. TOMM"},{"doi-asserted-by":"crossref","unstructured":"Levoy, M., and Hanrahan, P. (1996, January 4\u20139). Light field rendering. Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, New Orleans, LA, USA.","key":"ref_47","DOI":"10.1145\/237170.237199"},{"doi-asserted-by":"crossref","unstructured":"Gortler, S.J., Grzeszczuk, R., Szeliski, R., and Cohen, M.F. (1996, January 4\u20139). The lumigraph. Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, New Orleans, LA, USA.","key":"ref_48","DOI":"10.1145\/237170.237200"},{"unstructured":"Wetzstein, G. (2021, March 07). Synthetic Light Field Archive-MIT Media Lab. Available online: https:\/\/web.media.mit.edu\/~gordonw\/SyntheticLightFields\/.","key":"ref_49"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1137\/090771806","article-title":"Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions","volume":"53","author":"Halko","year":"2011","journal-title":"SIAM Rev."},{"key":"ref_51","first-page":"2825","article-title":"Scikit-learn: Machine learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"unstructured":"Musco, C., and Musco, C. (2015). Randomized block krylov methods for stronger and faster approximate singular value decomposition. arXiv.","key":"ref_52"},{"doi-asserted-by":"crossref","unstructured":"Cullum, J., and Donath, W.E. (1974, January 20\u201322). A block Lanczos algorithm for computing the q algebraically largest eigenvalues and a corresponding eigenspace of large, sparse, real symmetric matrices. Proceedings of the 1974 IEEE Conference on Decision and Control Including the 13th Symposium on Adaptive Processes, Phoenix, AZ, USA.","key":"ref_53","DOI":"10.1109\/CDC.1974.270490"},{"doi-asserted-by":"crossref","unstructured":"Golub, G.H., and Underwood, R. (1977, January 28\u201330). The block Lanczos method for computing eigenvalues. Proceedings of the Symposium Conducted by the Mathematics Research Center, the University of Wisconsin, Madison, WI, USA.","key":"ref_54","DOI":"10.1016\/B978-0-12-587260-7.50018-2"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1137\/0917055","article-title":"Efficient algorithms for computing a strong rank-revealing QR factorization","volume":"17","author":"Gu","year":"1996","journal-title":"Siam J. Sci. Comput."},{"unstructured":"Rerabek, M., and Ebrahimi, T. (2016, January 6\u20138). New light field image dataset. Proceedings of the 8th International Conference on Quality of Multimedia Experience (QoMEX), Lisbon, Portugal.","key":"ref_56"},{"doi-asserted-by":"crossref","unstructured":"Dansereau, D.G., Pizarro, O., and Williams, S.B. (2013, January 23\u201328). Decoding, calibration and rectification for lenselet-based plenoptic cameras. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Portland, OR, USA.","key":"ref_57","DOI":"10.1109\/CVPR.2013.137"},{"unstructured":"Pennebaker, W.B., and Mitchell, J.L. (1993). JPEG: Still Image Data Compression Standard, Kluwer Academic Publishers.","key":"ref_58"},{"unstructured":"Bjontegaard, G. (2021, March 07). Calculation of Average PSNR Differences between RD-Curves; Document VCEG-M33, ITU-T VCEG Meeting. Available online: https:\/\/www.itu.int\/wftp3\/av-arch\/video-site\/0104_Aus\/VCEG-M33.doc.","key":"ref_59"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/13\/4574\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:25:44Z","timestamp":1760163944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/13\/4574"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,4]]},"references-count":59,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["s21134574"],"URL":"https:\/\/doi.org\/10.3390\/s21134574","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2021,7,4]]}}}