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AMSR

{"forum": "5wBRXi9TPA", "submission_url": "https://openreview.net/forum?id=aJplLwLEg", "submission_content": {"authorids": ["jonathandaa@gmail.com", "linorack@gmail.com", "tomerweiss196@gmail.com", "sankethsai97@gmail.com", "ortalsen@gmail.com", "alexbronst@gmail.com"], "abstract": "Magnetic Resonance Imaging (MRI) is the gold standard of today's diagnostic imaging. The most significant drawback of MRI is the long acquisition time prohibiting its use in standard practice for some applications. Compressed sensing (CS) proposes to subsample the k-space (the Fourier domain dual to the physical space of spatial coordinates) leading to significantly accelerated acquisition. However, the benefit of compressed sensing has, to an extent, remained only theoretical because most of the sampling densities obtained through CS do not obey the stringent constraints of the MRI machine imposed in practice. Inspired by recent success of deep learning-based approaches for image reconstruction and ideas from computational imaging on learning-based design of imaging systems, we introduce 3D FLAT, a novel protocol to accelerate MRI acquisition in 3D. Our proposal leverages the entire 3D k-space to simultaneously learn a physically feasible acquisition trajectory with the reconstruction method. Experimental results suggest that 3D FLAT achieves a higher image quality for a given readout time compared to standard trajectories such as radial, stack-of-stars, or 2D learned trajectories. Furthermore, for the first time, we demonstrate the significant benefit of performing MRI acquisitions using non-Cartesian 3D trajectories over 2D non-Cartesian trajectories acquired slice-wise. ", "paper_type": "methodological development", "authors": ["Jonathan Alush-Aben", "Linor Ackerman", "Tomer Weiss", "Sanketh Vedula", "Ortal Senouf", "Alex Bronstein"], "track": "full conference paper", "keywords": ["Magnetic Resonance Imaging", "3D MRI", "fast image acquisition", "acceleration", "image reconstruction", "neural networks", "deep learning", "compressed sensing"], "title": "3D FLAT - Feasible Learned Acquisition Trajectories for Accelerated MRI", "paperhash": "alushaben|3d_flat_feasible_learned_acquisition_trajectories_for_accelerated_mri", "pdf": "/pdf/9bcc0cd6a988d99ed401a1eb8d62dc1f39995acd.pdf", "_bibtex": "@misc{\nalush-aben2020d,\ntitle={3D {\\{}FLAT{\\}} - Feasible Learned Acquisition Trajectories for Accelerated {\\{}MRI{\\}}},\nauthor={Jonathan Alush-Aben and Linor Ackerman and Tomer Weiss and Sanketh Vedula and Ortal Senouf and Alex Bronstein},\nyear={2020},\nurl={https://openreview.net/forum?id=aJplLwLEg}\n}"}, "submission_cdate": 1579955713997, "submission_tcdate": 1579955713997, "submission_tmdate": 1587172197631, "submission_ddate": null, "review_id": ["ldA-K3YYBu", "5vDCMIX_t", "KdCUxlsZCM", "J7IHi4f5ra"], "review_url": ["https://openreview.net/forum?id=aJplLwLEg&noteId=ldA-K3YYBu", "https://openreview.net/forum?id=aJplLwLEg&noteId=5vDCMIX_t", "https://openreview.net/forum?id=aJplLwLEg&noteId=KdCUxlsZCM", "https://openreview.net/forum?id=aJplLwLEg&noteId=J7IHi4f5ra"], "review_cdate": [1584480071080, 1584390999021, 1584178639144, 1584139362438], "review_tcdate": [1584480071080, 1584390999021, 1584178639144, 1584139362438], "review_tmdate": [1585229459911, 1585229459411, 1585229458904, 1585229458336], "review_readers": [["everyone"], ["everyone"], ["everyone"], ["everyone"]], "review_writers": [["MIDL.io/2020/Conference/Paper178/AnonReviewer1"], ["MIDL.io/2020/Conference/Paper178/AnonReviewer3"], ["MIDL.io/2020/Conference/Paper178/AnonReviewer4"], ["MIDL.io/2020/Conference/Paper178/AnonReviewer2"]], "review_reply_count": [{"replyCount": 0}, {"replyCount": 0}, {"replyCount": 0}, {"replyCount": 0}], "review_replyto": ["5wBRXi9TPA", "5wBRXi9TPA", "5wBRXi9TPA", "5wBRXi9TPA"], "review_content": [{"title": "Relevant application, straight-forward methodology, insufficient evaluation", "paper_type": "methodological development", "summary": "The paper proposes a methodology to optimize the 3d k-space trajectory for MRI reconstruction from data sampled below the Nyquist limit. Using soft physical constraints, the sampling trajectory is optimized such as to allow faithful reconstruction in an end-to-end model. The experiments are conducted using brain scans from the human connectome project.", "strengths": "* MRI reconstruction from undersampled data is a highly relevant problem.\n* The building blocks used in the paper (also the data) are well-understood and well-established.\n* The training is done end-to-end.", "weaknesses": "* The experiments are purely simulation-based; it is not clear how the trajectories perform in practice or even whether they can be implemented at all.\n* The simulation experiments are performed on small isotropic images of size 80^3 voxels, it remains unclear whether this setting is representative for larger resolutions.\n* Baseline experiments are missing e.g.\n a) CS + learned trajectories to verify whether the trajectories are specific to the NN reconstruction\n b) randomly perturbed trajectories + reconstruction to verify whether the performance of the learned trajectories is any better\n c) other NN reconstruction algorithms\n* Machine constraints on the first and second derivative of the k-space trajectory are only imposed in a soft way i.e. (1) via the loss function and (2) via a coarsened trajectory with a smoothing spline on top. It is unclear whether the constraints are met in practice and which of the two mechanisms guarantees that they are met.\n* Ablation experiments are missing.\n* The code of the methodology is not shared with the community and remains closed source which makes reproducibility very challenging; the data is public domain, though.\n* It remains unclear whether the obtained images are diagnostically useful e.g. an analysis of the highest error cases.\n* The optimisation is highly dependant on the initial trajectory.", "questions_to_address_in_the_rebuttal": "* In the Abstract in the last sentence, you claim that -- \"for the first time\" -- you demonstrate advantages of 3d acquisition over 2d acquisitions. This is a very bold statement not fully justified by your experiments. This alone, would be a strong paper. Please explain.\n* In Section 2.2 paragraph 2 you claim that the sampling operation is not differentiable. This statement is only true for nearest neighbor sampling but certainly not for multilinear and multicubic resampling. Please explain.\n* How do the learned k-space trajectories perform on high-res images?\n* How do the learned k-space trajectories perform on non-brain images?", "detailed_comments": "* Abstract: \"MRI is the gold standard of today's diagnostic imaging.\" -> This sentence is certainly not true in full generality as different applications have different preferred imaging modalities.\n* Intro, 4th paragraph: \"in an follow up\" -> \"in a follow up\"\n* Bibliography: Capitalization e.g. \"mri\"->\"MRI\" 5x, \"fourier\"->\"Fourier\"", "rating": "2: Weak reject", "justification_of_rating": "The empirical evaluation is not sufficiently complete to judge the possible merits of the proposed machinery. In particular, the comparison to already existing methods and proper baselines needs to be improved.", "confidence": "4: The reviewer is confident but not absolutely certain that the evaluation is correct", "recommendation": [], "special_issue": "no"}, {"title": "This paper presents a novel method to learn a k-space acquisition trajectory together with the corresponding reconstruction method. This is exciting since it is challenging the use of standard k-space trajectories (Cartesian, spiral, radial).", "paper_type": "methodological development", "summary": "Traditional MRI acquisition methods traverse k-space (Fourier space) in a serial Cartesian manner with trajectories in k-space being straight lines. Special sequences use radial lines, or spiral lines. This work relaxes this notion and permits any trajectory, with the constraint it should be physically possible (as defined by gradient specifications on the MRI scanner). The optimization is done using learning, and the method finds both the \u201coptimal\u201d trajectory, and the corresponding reconstruction method. This is an exciting idea worth exploring further.\n\n", "strengths": "The work connects nicely to previous literature on compressed sensing and recent literature on approaches using deep supervised learning. The proposed work include physical constraints such as maximum slew rate of magnetic gradients and upper bounds on the peak currents. This is novel and important. Including the physical limitation of the MRI scanner in the optimization is necessary to ensure clinical relevance. ", "weaknesses": "This is only a minor weakness, and more of a question: The paper demonstrates, as a proof-of-concept, that the learning-based design of feasible non-Cartesian 3D trajectories in MR imaging leads to better image reconstruction when compared to the off-the-shelf trajectories. This is all true, but the results seems to be confined to wiggly radial lines. It is not clear if this class of trajectories is enforced by the method, or truly is the way to go for optimal trajectories.\n", "rating": "4: Strong accept", "justification_of_rating": "The quest for optimal k-space sampling is still an active line of research. If learning can help us with the intuition of what k-space trajectories work better compared to current state-of-the art, this is welcome. As I understand it, this work is novel.\n", "confidence": "4: The reviewer is confident but not absolutely certain that the evaluation is correct", "recommendation": ["Oral"], "special_issue": "yes"}, {"title": "Incorrect premise and inadequate evaluation", "paper_type": "methodological development", "summary": "This paper describes a data-driven method to design 3D k-space trajectories under constraints on the gradient amplitude and slew rate. The trajectory is designed jointly with the reconstruction method. The method is tested using human connectome project data. \n\nI do not believe the work is significant. ", "strengths": "I do not believe this work has any real strengths. There are many problems. \n\nNote to organizing committee: I think it's a bad idea for you to require 200 characters for this text field. I don't have that much to say.", "weaknesses": "This paper makes a lot of major mistakes.\n\n*The papers' main premise is that \"many CS-based methods are not practically implementable on real MRI machines because of the stringent hardware constraints to which random sampling of the k-space does not adhere.\" This is a very bold statement because it basically implies that the past ~15 years of image reconstruction research were all a waste of time and focused on infeasible scenarios. Regrettably, the papers' premise is incorrect -- there are many MRI methods that use random sampling and have been practically implemented. This is good for the MRI field because it means that the past ~15 years were not a waste of time. But this is a critical misunderstanding of the literature.\n\n*The paper claims that \"to the best of our knowledge, this is the first attempt of data-driven design of feasible 3D trajectories in MRI.\" There are existing data-driven design methods that can produce feasible 3D MRI trajectories, including:\n\nHaldar JP, Kim D. OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI. IEEE Trans Med Imaging. 2019 Jul;38(7):1545-1558. doi: 10.1109/TMI.2019.2896180. \n\nCagla Deniz Bahadir, Adrian V. Dalca, and Mert R. Sabuncu. Learning-based optimization of the under-sampling pattern in mri. In Albert C. S. Chung, James C. Gee, Paul A. Yushkevich, and Siqi Bao, editors, Information Processing in Medical Imaging, pages 780{792, Cham, 2019. Springer International Publishing.\n\n*The paper evaluates performance on an unrealistic dataset. The human connectome project does not provide k-space data, so the paper must be simulating artificial k-space data from images. These images will have no phase and no multichannel features which makes them very simple compared to the real case. Simulations that are this unrealistic can be very misleading\n\n*The trajectories shown in this paper are very nonsmooth. These may be feasible in simulation, but they probably aren't feasible on real machines because of eddy currents and trajectory calibration problems.\n\n*The paper describes 3D stack of stars as \"today's gold standard\". 3D stack of stars is definitely not a gold standard for brain imaging. Wave-CAIPI is an obvious more recent alternative:\n\nBilgic B, Gagoski BA, Cauley SF, et al. Wave-CAIPI for highly accelerated 3D imaging. Magn Reson Med. 2015;73(6):2152\u20132162. doi:10.1002/mrm.25347\n\nPolak D, Setsompop K, Cauley SF, et al. Wave-CAIPI for highly accelerated MP-RAGE imaging. Magn Reson Med. 2018;79(1):401\u2013406. doi:10.1002/mrm.26649\n\nKim TH, Bilgic B, Polak D, Setsompop K, Haldar JP. Wave-LORAKS: Combining wave encoding with structured low-rank matrix modeling for more highly accelerated 3D imaging. Magn Reson Med. 2019;81(3):1620\u20131633. doi:10.1002/mrm.27511\n\n*The paper claims that previous methods use a maximum a posteriori formulation. This is also incorrect -- very few MRI authors use a Bayesian interpretation of regularization.\n\n*The paper claims to demonstrate the true merit of 3D over 2D. The merits of 3D over 2D are classical and well known, and the paper does not offer any new insights.\n\n*The paper claims that sampling is non differentiable because it involves rounding. How does bilinear interpolation involve rounding? Bilinear interpolation amounts to convolving the sample positions with an interpolation kernel and then evaluating the values at the sample positions. This is easily differentiable at most sampling locations.\n\n*The paper cites (Lauterbur 1973) for 3D stack of stars. Lauterbur's paper does not discuss 3D stack of stars.\n\n*The color scheme used for Figure 4 makes it very hard to see things.", "questions_to_address_in_the_rebuttal": "The literature review is inaccurate and needs to be rewritten. The experiments need to be redone with real multi-coil k-space data.", "rating": "1: Strong reject", "justification_of_rating": "This paper makes major mistakes and does not make a useful contribution. Even worse, the paper makes misleading statements and fails to disclose that the simulations are unrealistic. This sets a bad example for other researchers.", "confidence": "5: The reviewer is absolutely certain that the evaluation is correct and very familiar with the relevant literature", "recommendation": [], "special_issue": "no"}, {"title": "Review of 3D FLAT - Feasible Learned Acquisition Trajectories for Accelerated MRI", "paper_type": "both", "summary": "The authors propose to accelerate MRI acquisition by optimizing sampling trajectories in 3D using neural networks. It is a very original work and the authors provide detailed and convincing analyses. ", "strengths": "-The manuscript addresses a very relevant problem: acceleration of MRI acquisition\n-The approach is very pragmatic: the authors try to incorporate best physical constraints of the acquisition\n-Search for trajectories in 3D opens a meaningful new research direction\n-The manuscript is very well written\n-limitations are cleared stated\n", "weaknesses": "-the proposed algorithm needs to be trained (some deep learning algorithms for MR reconstruction do not)\n-experiments performed with simulated data\n-no statistical test to verify assumptions\n-evaluation in a single dataset\n", "detailed_comments": "Minor comments:\n\n-1st paragraph section 2:\u201cspace domain\u201d => spatial\n-RF is not defined (Radiofrequency)\n-\u201dn\u201d is not defined\n-Figure 2: it seems the reconstruction of the 3D FLAT has more brain atrophy. Am I making this up? Could it be due to some bias in the training dataset?", "rating": "4: Strong accept", "justification_of_rating": "Interesting method with potentially strong practical and methodological impact. Substantial analysis of results. Convincing results and good discussion. ", "confidence": "3: The reviewer is fairly confident that the evaluation is correct", "recommendation": ["Oral"], "special_issue": "yes"}], "comment_id": ["KFfanTa2VTG", "CCNADXjv_Z4", "CibIFYEM1gT", "1UTRYplD4c", "9TGOZB-dAiy", "VsU2ffWfpz-", "UwtlpYVleMJ", "giYusP0AUvy"], "comment_cdate": [1585243631237, 1585243558113, 1585243472472, 1585240586217, 1585243069533, 1585239580676, 1585241538267, 1585240541223], "comment_tcdate": [1585243631237, 1585243558113, 1585243472472, 1585240586217, 1585243069533, 1585239580676, 1585241538267, 1585240541223], "comment_tmdate": [1585585207626, 1585585193702, 1585585175994, 1585303488245, 1585286991383, 1585252921215, 1585251850865, 1585243739522], "comment_readers": [["everyone"], ["everyone"], ["everyone"], ["everyone", "MIDL.io/2020/Conference/Paper178/Reviewers/Submitted", "MIDL.io/2020/Conference/Paper178/Authors"], ["everyone", "MIDL.io/2020/Conference/Paper178/Reviewers/Submitted", "MIDL.io/2020/Conference/Paper178/Authors"], ["everyone", "MIDL.io/2020/Conference/Paper178/Reviewers/Submitted", "MIDL.io/2020/Conference/Paper178/Authors"], ["everyone", "MIDL.io/2020/Conference/Paper178/Reviewers/Submitted", "MIDL.io/2020/Conference/Paper178/Authors"], ["MIDL.io/2020/Conference/Paper178/Reviewers/Submitted", "MIDL.io/2020/Conference/Paper178/Authors", "everyone"]], "comment_writers": [["MIDL.io/2020/Conference/Paper178/Authors", "MIDL.io/2020/Conference"], ["MIDL.io/2020/Conference/Paper178/Authors", "MIDL.io/2020/Conference"], ["MIDL.io/2020/Conference/Paper178/Authors", "MIDL.io/2020/Conference"], ["MIDL.io/2020/Conference/Paper178/Authors", "MIDL.io/2020/Conference"], ["MIDL.io/2020/Conference/Paper178/Authors", "MIDL.io/2020/Conference"], ["MIDL.io/2020/Conference/Paper178/Authors", "MIDL.io/2020/Conference"], ["MIDL.io/2020/Conference/Paper178/Authors", "MIDL.io/2020/Conference"], ["MIDL.io/2020/Conference/Paper178/Authors", "MIDL.io/2020/Conference"]], "comment_reply_content": [{"replyCount": 0}, {"replyCount": 0}, {"replyCount": 0}, {"replyCount": 0}, {"replyCount": 0}, {"replyCount": 0}, {"replyCount": 0}, {"replyCount": 0}], "comment_content": [{"title": "Response to reviewer #4 (3/3) ", "comment": "*The paper claims to demonstrate the true merit of 3D over 2D. The merits of 3D over 2D are classical and well known, and the paper does not offer any new insights.\n\nThere are three common paradigms in designing 3D acquisitions: \n1. Designing a feasible 2D Cartesian trajectory, acquire using it slice-wise. The works that fall into the category are: [1], [2], [3]\n2. Designing feasible 2D non-Cartesian trajectories and acquiring them slice-wise. The following methods fall under this category: [4], [5]\n3. Designing an arbitrary sampling density in 2D and acquiring the complete line of k-space in the third dimension ([6], [7] and similar works).\nOur work and 3D SPARKLING [8] proposes a fourth paradigm where we aim to design non-Cartesian 3D trajectories by leveraging all the available degrees of freedom. Although it might seem obvious that our paradigm must result in most efficient trajectories, given that it is the most general one and paradigms 1, 2 & 3 are special cases of our methodology; it is non-trivial to find such trajectories. In fact, in 3D SPARKLING, the authors concluded that the 2D non-Cartesian trajectories acquired slice-wise (paradigm 2) outperformed the 3D non-Cartesian ones. Whereas, we propose a framework to design 3D non-Cartesian trajectories jointly with the reconstruction, and demonstrate that they outperform the paradigm 2 by a clear margin; we also discussed in-depth what merits our method, 3D FLAT, possesses when compared to 3D SPARKLING. We believe this is a valuable insight and lays the ground for many future directions in this emerging field of k-space trajectory design. We modified the introduction reflecting this discussion.\n\n1. Weiss, Tomer et al. \u201cLearning Fast Magnetic Resonance Imaging.\u201d arXiv e-prints, art.arXiv:1905.09324, May 2019b.\n2. Jin, Kyong Hwan et al. \u201cSelf-Supervised Deep Active Accelerated MRI.\u201d arXiv preprint arXiv:1901.04547, 2019.\n3. Zhang, Zizhao et al. \u201cReducing Uncertainty in Undersampled MRI Reconstruction With Active Acquisition.\u201d The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019, pp. 2049-2058\n4. Weiss, Tomer et al. \u201cPILOT: Physics-Informed Learned Optimal Trajectories for Accelerated MRI.\u201d arXiv:1909.05773, Sep 2019a.\n5. Lazarus, Carole et al. \u201cSPARKLING: variable-density k-space filling curves for accelerated T2*-weighted MRI.\u201d Magnetic Resonance in Medicine, 2019a.\n6. Bahadir, Cagla et al. \u201cLearning-Based Optimization of the Under-Sampling Pattern in {MRI}.\u201d Information Processing in Medical Imaging. Springer International Publishing. 2019\n7. J. P. Haldar and D. Kim, \u201cOEDIPUS: An experiment design framework for sparsity-constrained MRI.\u201d IEEE transactions on medical imaging., 2019.\n8. Lazarus, Carole et al. \u201c3D SPARKLING trajectories for high-resolution T2*-weighted Magnetic Resonance Imaging.\u201d 2019\n\n\n*The paper claims that sampling is non-differentiable because it involves rounding. How does bilinear interpolation involve rounding? Bilinear interpolation amounts to convolving the sample positions with an interpolation kernel and then evaluating the values at the sample positions. This is easily differentiable at most sampling locations.\n\nWe agree. In fact, we use the differentiability of the interpolation to get meaningful gradients on the sampling points. Our intention was to convey that sampling alone without interpolation would lead to meaningless gradients, although some autograd tricks allow for gradient propagation through sampling operations. We clarified it in the text. \n\n*The paper cites (Lauterbur 1973) for 3D stack of stars. Lauterbur's paper does not discuss 3D stack of stars.\nWe thank the reviewer for pointing it out, this is a misunderstanding on our part. We corrected it in the text.\n\n*The color scheme used for Figure 4 makes it very hard to see things.\n\nOur intention for adding this figure is to plot the effective sampling density of the learned trajectories. \n"}, {"title": "Response to reviewer #4 (2/3) ", "comment": "*The trajectories shown in this paper are very nonsmooth. These may be feasible in simulation, but they probably aren't feasible on real machines because of eddy currents and trajectory calibration problems.\n\nThe learned trajectories are smooth. However, due to the limitations of 3D visualization it sometimes can not be visualized properly, because one of the dimensions gets skewed out of proportion. A zoomed-in trajectory is presented in Fig. 7 in the supplementary materials: notice the increased sampling density at the high curvature parts of the black curve. It is true that we do not take into account eddy-currents and trajectory calibration. Trajectory calibration can be tackled by employing some grid-free learned inverse Fourier transform, as done in AUTOMAP [1]. We leave these two issues for future work. By modeling these issues as constraints (similar to what we did for max. slew rate & gradient), into the reconstruction pipeline, we believe the learned trajectories will be resilient to these perturbations and be of practical use. \nWe have made our code and the trajectories used for this paper available at https://github.com/3d-flat/3dflat/.\n\n[1] Zhu, Bo, et al. \"Image reconstruction by domain-transform manifold learning.\" Nature 555.7697 (2018): 487-492.\n\n*The paper describes 3D stack of stars as \"today's gold standard\". 3D stack of stars is definitely not a gold standard for brain imaging. Wave-CAIPI is an obvious more recent alternative:\n\nWe thank the reviewer for pointing out these references. The references seem very interesting and relevant. To the best of our understanding, the motivation for the Wave-CAIPI method is to avoid aliasing, and for that, they apply a cork-screw trajectory in k-space instead of sampling in a Cartesian way. In a sense, our methodology can be viewed as a generalization of this approach. The reason being: when the trajectories are learned together with the reconstruction network, they are automatically modified in order to be optimal with respect to the end task. During the training, if there appears to be aliasing (as was the case in Wave-CAIPI), the network would avoid these trajectories if they result in poor end-task performance. In our experiments, we found that for any initialization, our method found a trajectory that is the more optimal one. This makes us believe that this cork-screw trajectory can serve as an initialization for our method and can be optimized jointly with the network to produce further improvements. The rationale for making such an argument is as follows: most initialized trajectories are heuristically hand-crafted and are therefore not necessarily the global optimum of this very high-dimensional k-space trajectory design problem. Therefore, any initialized trajectory has in its vicinity (w.r.to some metric) a locally optimal trajectory which can be found through our method by task-driven optimization. We will add this discussion to the paper. \n\nBilgic B, Gagoski BA, Cauley SF, et al. Wave-CAIPI for highly accelerated 3D imaging. Magn Reson Med. 2015;73(6):2152\u20132162. doi:10.1002/mrm.25347\n\nPolak D, Setsompop K, Cauley SF, et al. Wave-CAIPI for highly accelerated MP-RAGE imaging. Magn Reson Med. 2018;79(1):401\u2013406. doi:10.1002/mrm.26649\n\nKim TH, Bilgic B, Polak D, Setsompop K, Haldar JP. Wave-LORAKS: Combining wave encoding with structured low-rank matrix modeling for more highly accelerated 3D imaging. Magn Reson Med. 2019;81(3):1620\u20131633. doi:10.1002/mrm.27511\n\n*The paper claims that previous methods use a maximum a posteriori formulation. This is also incorrect -- very few MRI authors use a Bayesian interpretation of regularization.\n\nMost previous prior-based methods that impose regularization on the latent images (such as, total variation, sparsity w.r.to a dictionary, and recently, deep image priors) can be easily interpreted via the maximum-a-posteriori formulation in a Bayesian framework. This interpretation is exact and has no loss in generality, although the authors of the respective papers do not necessarily interpret the same way as we do. We modified the statement to \u201cSome previous methods use a maximum-a-posteriori...\u201d.\n\n"}, {"title": "Response to reviewer #4 (1/3) ", "comment": "We thank Reviewer #4 for their comments. Below we address all the raised issues.\nFirst of all, we apologize for the miscommunication. Our premise was probably not well formulated and therefore misunderstood. We obviously do not argue or believe that the previous research was a waste of time. Please note that traditionally, with the compressed sensing-based approaches the sampling densities attained in 2D is not physically maneuverable (in 2D) by the machine because it does not adhere to maximum slew-rate and maximum gradient constraints. A simple workaround to still utilize these 2D densities is by sampling a complete line along the third dimension, and acquire separate shots at each of these sampling points. This is suboptimal because it does fully exploit the flexibility we have in the 3rd dimension. \n\nTherefore, we believe that the value of variable density sampling in 3D was not explored to the fullest extent. In fact, this very issue is of emerging interest in the MRI community, please see SPARKLING, 3D SPARKLING and the follow-up works. We bring together tools from deep learning, and ideas from computational imaging to address this issue to exploit this additional degree of freedom. We propose a framework that treats trajectories as a learnable parameter in the end-to-end differentiable acquisition-reconstruction pipeline and constrain the design space of the trajectories by enforcing machine constraints. We modified the introduction statements in our paper to reflect this discussion.\n\n*The paper claims that \"to the best of our knowledge, this is the first attempt of data-driven design of feasible 3D trajectories in MRI.\" There are existing data-driven design methods that can produce feasible 3D MRI trajectories, including:\n\nHaldar JP, Kim D. OEDIPUS: An Experiment Design Framework for Sparsity-Constrained MRI. IEEE Trans Med Imaging. 2019 Jul;38(7):1545-1558. doi: 10.1109/TMI.2019.2896180. \n\nCagla Deniz Bahadir, Adrian V. Dalca, and Mert R. Sabuncu. Learning-based optimization of the under-sampling pattern in MRI. In Albert C. S. Chung, James C. Gee, Paul A. Yushkevich, and Siqi Bao, editors, Information Processing in Medical Imaging, pages 780{792, Cham, 2019. Springer International Publishing.\n\nIndeed, both of the above papers learned sampling densities in 2D, but note that they do not actually discuss their practical deployability in 3D. One way to translate the sampling densities into feasible 3D trajectories by sampling the third dimension fully. We can denote such approaches as Cartesian 3D sampling. However, in our framework, this third degree of freedom is exploited, and our 2D vs. 3D experiments suggest that adding this 3rd dimension to optimization provides a significant improvement in the reconstruction performance. Therefore as rightly pointed out, we shall change our novelty statement to \u201cdata-driven design of 3D non-Cartesian trajectories in MRI\u201d to better reflect the contributions of the work.\n\n*The paper evaluates performance on an unrealistic dataset. The human connectome project does not provide k-space data, so the paper must be simulating artificial k-space data from images. These images will have no phase and no multichannel features which makes them very simple compared to the real case. Simulations that are this unrealistic can be very misleading.\n\nThis is indeed a limitation of our work. The reason why we chose to work with the HCP dataset is because of its uniform sampling across all dimensions, this is unavailable in, for example, the NYU-FAIR fastMRI dataset (that provides raw k-space data) which does not allow for efficient/realistic resampling in the z dimension. Since our method works in 3D, it is also data-intensive, we were not able to find a large scale dataset that has raw k-space data available other than the fastMRI dataset. Furthermore, the margins we demonstrate are >~1.2dB in PSNR averaged over 105 volumes, which we believe is a non-marginal improvement. This has been resulted only due to the learning of trajectories, keeping all the other blocks consistent. Consequently, it makes us believe that our method might produce reasonable improvements on raw multi-coil k-space data.\n\nWe understand that the trajectories that we obtain are not of immediate clinical use without further experimentation and retraining on raw datasets. However, we believe our work makes a methodical contribution to the community by demonstrating an initial proof-of-concept and providing a framework to design non-Cartesian 3D trajectories that are implementable by the machine. We, therefore, believe that our work, given all its known limitations, would still be of interest to the MIDL community since it opens doors for many interesting future research directions. That said, to be clear in our message, we shall emphasize this issue about data inaccuracy throughout the paper, in the abstract, introduction, and in conclusion.\n\n\n"}, {"title": "Reply to reviewer #3", "comment": "We thank Reviewer #3 for their encouraging comments! Below we address all the raised issues.\n\nWeaknesses: This is only a minor weakness, and more of a question: The paper demonstrates, as a proof-of-concept, that the learning-based design of feasible non-Cartesian 3D trajectories in MR imaging leads to better image reconstruction when compared to the off-the-shelf trajectories. This is all true, but the results seems to be confined to wiggly radial lines. It is not clear if this class of trajectories is enforced by the method, or truly is the way to go for optimal trajectories.\n\nWe believe that this is some limitation of our method. The learned trajectories sometimes stay in similar general shape as the initialization. This probably shows that we did not yet find the global minimum. Similar observations have been made in PILOT [1] and SPARKLING [2]. \nWe assume the reason for this phenomenon is as follows: most initialized trajectories are heuristically hand-crafted and are therefore not necessarily the global optimum of this very high-dimensional k-space trajectory design problem. Therefore, any initialized trajectory has in its vicinity (w.r.to some metric) a locally optimal trajectory (that adheres to this constraint) which is probably being found through our method by task-driven optimization, although the design space consists of all possible 3D non-Cartesian trajectories (that obey machine constraints). \n\nAn initial approach to counter this problem of local minima was proposed in [1]. We plan to take a similar approach in our future work.\n\n[1] Weiss, Tomer et al. \u201cPILOT: Physics-Informed Learned Optimal Trajectories for Accelerated MRI.\u201d arXiv:1909.05773, Sep 2019a.\n\n[2] Lazarus, Carole et al. \u201cSPARKLING: variable-density k-space filling curves for accelerated T2*-weighted MRI.\u201d Magnetic Resonance in Medicine, 2019a.\n\n"}, {"title": "Response to reviewer #1 (3/3) ", "comment": "* How do the learned k-space trajectories perform on non-brain images?\n\nWe expect that trajectories designed would be specific to the chosen anatomy, and would not be exactly transferrable due to the difference k-space energy distributions for different anatomies. The rationale for this argument is as follows: as can be seen in Figure 4, the samples of the learned trajectories are approximately isotropically distributed around the origin; we believe this isotropy is a property of the brain dataset. However, if we observe results of 2D learned sampling densities and 2D non-Cartesian trajectories of knee MRI scans reported by LOUPE [1] and PILOT [2], we can notice that resulting sampling densities of the knee are rather anisotropic and differ from the brain images. \n\n[1] Bahadir et al., \u201cAdaptive Compressed Sensing MRI with Unsupervised Learning.\u201d arXiv preprint arXiv:1907.11374\n[2] Weiss et al., \u201cPILOT: Physics-Informed Learned Optimal Trajectories for Accelerated MRI.\u201d arXiv:1909.05773.\n\nDetailed Comments: * Abstract: \"MRI is the gold standard of today's diagnostic imaging.\" -> This sentence is certainly not true in full generality as different applications have different preferred imaging modalities.\n\nWe change it to \u201cMagnetic Resonance Imaging (MRI) has long been considered to be among ``the gold standards\" of diagnostic medical imaging.\u201d\n\n"}, {"title": "Reply to reviewer #1 (1/3)", "comment": "We thank Reviewer #1 for their comments. Below we address all the raised issues.\n\n* Regarding the experiments being simulation-based:\n\nWe agree with this criticism and leave the evaluation of the proposed trajectories in a real MRI machine to future work. Regarding implementability, two major and immediate constraints that a trajectory needs to adhere to in order to be physically feasible are the maximum slew-rate and maximum gradient bounds of the machine. We tackled this issue, and proposed a method to explore the design space of trajectories that obey these constraints. Similarly to what has been done in SPARKLING [1], we can translate our trajectories into gradient protocols, which can be programmed into machines, as long as they obey these machine constraints. \n\nHowever, as rightly pointed out, what is indeed a limitation of our method is that it is simulation-based, and it does not take into account the real-life scenarios such as decaying SNR during the shot, sampling errors, and therefore our trajectories might be not directly deployed (to achieve good performance) without retraining on raw-data acquired from real machines. We believe that our trajectories will be resilient to decaying SNR because each individual shot is 30ms; there have been approaches to tackle sampling errors as done in AUTOMAP [2], where the authors used a fully-connected network to perform grid-free inverse fourier transform that deemed resilient to sampling errors. \n\nTherefore, we believe that, despite the limitations, our method bears value as proof-of-concept \nshowing that trajectory optimization jointly with reconstruction has non-trivial promise. That said, performing experiments on real machines is necessary for the next steps of the research and to evaluate the clinical value of the proposed method, but they are out of scope of the current proof-of-concept.\n\t\n[1] Lazarus, Carol et al. \u201cSPARKLING: variable-density k-space filling curves for accelerated T2*-weighted MRI.\u201d Magnetic Resonance in Medicine, 2019a.\n\n[2] Zhu, Bo, et al. \"Image reconstruction by domain-transform manifold learning.\" Nature 555.7697 (2018): 487-492.\n\n* The simulation experiments are performed on small isotropic images of size 80^3 voxels, it remains unclear whether this setting is representative for larger resolutions.\n\nThe experiments were performed with low-res images due to performance considerations. The main drawback of using NN with 3D images is the memory required to process them. Less resource-intensive reconstruction methods should be used for higher resolutions - for example a 2D NN serialized slicewise. Appropriate optimization will solve these issues makeing the same method applicable to higher resolution data.\n\n* Baseline experiments are missing e.g.\n a) CS + learned trajectories to verify whether the trajectories are specific to the NN reconstruction\n b) randomly perturbed trajectories + reconstruction to verify whether the performance of the learned trajectories is any better\n c) other NN reconstruction algorithms\n\n(a) An experiment evaluating CS + learned trajectory was presented in the main paper and in Table I of the appendix, the result showed that the learned trajectories are better also under the CS reconstruction. We believe that the trajectory learning also led to a generally superior sampling density in k-space (see Figure 4), and CS based solvers already benefit from it. \n(b) and (c) can indeed strengthen our claims but due to the time constraints, we deferred these experiments to future work.\n\n* Regarding how machine constraints are imposed: \n\nWe enforce the penalty through hinge-loss on the gradient and slew-rate. Hinge-loss vanishes when the constraints are met, and we report results in which these penalties are strictly zero. As we mentioned in the paper in the beginning of Section 3, all the trajectories reported in the paper obey machine constraints. In future work, we will study methods that explicitly impose constraints during the training process. \n\n* Regarding our code:\n\nWe posted our code and a few sample output trajectories on github https://github.com/3d-flat/3dflat/\n\n* It remains unclear whether the obtained images are diagnostically useful:\n\nIn Figure 3, we can notice in the error bars that even the highest error (w.r.to PSNR, SSIM) volumes performed better with the learned trajectories than the fixed ones, meaning that important details are recovered with the learned trajectories than the fixed ones, even in the worst case. Figures 8, 9 depict that the learned trajectories recover a significant amount of details when compared to the fixed ones. However, a larger-scale visual study (by taking a mean-opinion-scores from physicians) needs to be conducted to actually evaluate the clinical significance of the method. \n"}, {"title": "Response to reviewer #1 (2/3)", "comment": "* The optimisation is highly dependant on the initial trajectory.\n\nUnfortunately, this is also a problem encountered by SPARKLING [1] and PILOT [2], that approached trajectory optimization while obeying machine constraints.\n\nOne approach to counter this issue was proposed in PILOT. The authors perform a two-stage procedure, which they refer to as PILOT-TSP, where first, they optimize for the optimal sampling density, reorder the points by solving a traveling-salesman problem, and then design a trajectory by enforcing machine constraints. This led to partially alleviate the problem of initialization. However, it is still a promising open direction to extend such ideas to multi-shot trajectory design (as it is in our case), and to 3D. We plan to explore this direction in future work.\n\nMore generally, beyond MRI, the heavy dependence on initialization is in fact one of the open problems in similar joint forward-inverse modeling problems encountered in other imaging modalities, such as accelerated ultrasound imaging [3].\n\n[1] Lazarus, Carol et al. \u201cSPARKLING: variable-density k-space filling curves for accelerated T2*-weighted MRI.\u201d Magnetic Resonance in Medicine, 2019a.\n[2] Weiss, Tomer et al. \u201cPILOT: Physics-Informed Learned Optimal Trajectories for Accelerated MRI.\u201d arXiv:1909.05773, Sep 2019a.\n[3] Vedula, Sanketh et al. \u201cLearning beamforming in ultrasound imaging.\u201d International Conference on Medical Imaging with Deep Learning, 2019.\n\nQuestions To Address In The Rebuttal: \n* In the Abstract in the last sentence, you claim that -- \"for the first time\" -- you demonstrate advantages of 3d acquisition over 2d acquisitions. This is a very bold statement not fully justified by your experiments. This alone, would be a strong paper. Please explain.\n\nWe mention that we demonstrate the merit of \u201cperforming MRI acquisitions using non-Cartesian 3D trajectories over 2D non-Cartesian trajectories acquired slice-wise\u201d. This claim is supported by the quantitative results reported in Section 3. We consider the three following scenarios:\n- 2D learning: the trajectory is initialized with 2D-SOS stacked across slices. We let the trajectory evolve only within x and y; while keeping the z coordinate fixed. This leads to 2D non-Cartesian trajectories that can be acquired slice-wise.\n- 3D learning: the trajectory is initialized as in the above case but the z coordinate is allowed to be modified. Therefore, the resulting trajectory is a 3D non-Cartesian trajectory.\n- Learned radial: we initialize the trajectory with radial trajectory, which is essentially a spoke in the 3D sphere, and then is allowed to update in all dimensions, which also results in a 3D non-Cartesian trajectory.\nOur results suggest that, over a test set consisting of 105 volumes, the above-described 3D learned and learned radial (2nd, 3rd) cases outperformed by >1.2dB -- we believe this is a non-trivial, significant improvement. Since the reconstruction network and the rest of the pipeline are exactly the same for all the above cases, we believe that it is fair to contribute this improvement to learning 3D non-Cartesian trajectories. \n\nThe main reason why we made such a claim was because in 3D SPARKLING, the conclusion by the authors was the opposite: 2D non-Cartesian trajectories acquired slice-wise outperformed 3D non-Cartesian trajectories. We discussed in-depth about this issue in Section 3 in our paper. \n\nHowever, in a general sense, we understand that \u201cfor the first time\u201d might be a very bold claim for a work that has been tested only retrospectively, i.e., only in simulations and not by acquiring the data by coding the trajectories onto a real machine. We toned down this claim by explicitly mentioning that we perform retrospective experiments in the revised manuscript.\n\n* In Section 2.2 paragraph 2 you claim that the sampling operation is not differentiable. This statement is only true for nearest neighbor sampling but certainly not for multilinear and multi cubic resampling. Please explain.\n\nThis is a slight miscommunication on our side. Interpolation is performed in 2 steps - sampling (non-differentiable) and weighted average (differentiable). We wanted to emphasize that the gradient flowing from the second step is enough, and in fact, it enables meaningful gradients for trajectory learning. We clarified it in the text.\n\n* How do the learned k-space trajectories perform on high-res images?\n\nAs we mentioned in the paper, the only issue that limited us to scale to higher-resolution is the computational complexity of the reconstruction network. We believe once this is resolved, our method would scale to finer grids. Trajectories wise, the search space of the k-space grows significantly, and it would be then interesting to see what trajectory the optimization would result in. \n\n"}, {"title": "Reply to reviewer #2", "comment": "We thank Reviewer #2, for their encouraging comments. Below we address all the raised issues.\n\nWeaknesses: \n-the proposed algorithm needs to be trained (some deep learning algorithms for MR reconstruction do not)\n\nThis is true. We are indeed limited by training and the datasets used for training. However, it is important to note that we do not provide a solution for MR reconstruction method, the inverse problem, but a framework to jointly train the forward and inverse models. It is indeed interesting to think of cases where our approach can be combined with unsupervised/self-supervised inverse problem solvers.\n\n-experiments performed with simulated data\n-no statistical test to verify assumptions\n-evaluation in a single dataset\n\nWe agree. This is indeed a limitation of our method, and since we perform retrospective experiments, it does not take into account the real-life scenarios such as decaying SNR during a shot, sampling errors, and therefore our trajectories might be not directly deployed (to achieve good performance) without retraining on raw-data acquired from real machines. We were not able to find a large enough dataset as the HCP datasets. We considered the NYU-FAIR fastMRI challenge dataset, but in that dataset the z axis was very coarsely sampled that would lead to unrealistic sampling along one dimension. We believe that more rigorous testing is required, therefore we added a point emphasizing this as a limitation in the abstract, introduction and in the conclusion. Despite all the limitations, we believe that our work can be a methodical contribution, and would lead to many open research directions.\n\nDetailed Comments: Minor comments:\n\n-1st paragraph section 2:\u201cspace domain\u201d => spatial\n-RF is not defined (Radiofrequency)\n-\u201dn\u201d is not defined\nThanks for the comments. We added explanation to the above notation, and made the edits. \n-Figure 2: it seems the reconstruction of the 3D FLAT has more brain atrophy. Am I making this up? Could it be due to some bias in the training dataset?\nWe believe that this is due to the down-sampling we perform on the images.\n"}], "comment_replyto": ["CCNADXjv_Z4", "CibIFYEM1gT", "KdCUxlsZCM", "5vDCMIX_t", "UwtlpYVleMJ", "ldA-K3YYBu", "VsU2ffWfpz-", "J7IHi4f5ra"], "comment_url": ["https://openreview.net/forum?id=aJplLwLEg&noteId=KFfanTa2VTG", "https://openreview.net/forum?id=aJplLwLEg&noteId=CCNADXjv_Z4", "https://openreview.net/forum?id=aJplLwLEg&noteId=CibIFYEM1gT", "https://openreview.net/forum?id=aJplLwLEg&noteId=1UTRYplD4c", "https://openreview.net/forum?id=aJplLwLEg&noteId=9TGOZB-dAiy", "https://openreview.net/forum?id=aJplLwLEg&noteId=VsU2ffWfpz-", "https://openreview.net/forum?id=aJplLwLEg&noteId=UwtlpYVleMJ", "https://openreview.net/forum?id=aJplLwLEg&noteId=giYusP0AUvy"], "meta_review_cdate": 1585623178518, "meta_review_tcdate": 1585623178518, "meta_review_tmdate": 1585623178518, "meta_review_ddate ": null, "meta_review_title": "MetaReview of Paper178 by AreaChair1", "meta_review_metareview": "The methodology presented is interesting. The main limitation seems to be its practical uses in the real machine. I suggest acceptance at this point but hope the authors may consider to improve it for real applications. Another concern I have is the complex-valued nature of the data, have you used complex convolution like Wang's group? Please properly refer to DeepcomplexMRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution and Accelerating magnetic resonance imaging via deep learning; These works need to be properly cited as well. ", "meta_review_readers": ["everyone"], "meta_review_writers": ["MIDL.io/2020/Conference/Program_Chairs", "MIDL.io/2020/Conference/Paper178/Area_Chairs"], "meta_review_reply_count": {"replyCount": 0}, "meta_review_url": ["https://openreview.net/forum?id=aJplLwLEg&noteId=XjkVYm-W1rP"], "decision": "accept"}