{"id":"ba7770c0-cd3f-4b72-9daf-04f57e17a661","arxiv_id":"2501.01482","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"DISCUS applies group sparsity to deep image prior code vectors, letting the method discover the low-dimensional manifold of a dynamic image series and improving single-shot cardiac MRI reconstruction.","lead":"This paper introduces DISCUS, an unsupervised method for reconstructing series of heart MRI images from undersampled data without needing fully sampled training images. It trains a neural network to map sparse shared code values to each frame, and the authors report that it outperforms several existing methods on simulations and real patient scans.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed discovery of manifold dimensionality is not established: group sparsity manufactures sparsity, no nonzero threshold is specified, and Study I already reports 8/10 success and no disentanglement.","rationale":"The empirical reconstruction comparison is the strongest part of the paper: three studies with multiple acceleration factors, a prospective blinded reader study, and an ablation showing that group sparsity improves over DGS. My concern targets the headline scientific claim of dimensionality discovery rather than the reconstruction pipeline. The support of z_t is a regularized parameter count, not an invariant of the data manifold; without an identifiability argument or a threshold rule, describing this as 'discovery' is overstated. This matters because it is the stated contrast with Gen-SToRM and related manifold methods, and because it underlies the claim that the method needs no pre-specified manifold dimension. It is not fatal to the engineering contribution: even if the support count is an imperfect proxy, the joint reconstruction may still be clinically useful and superior to per-frame DIP. That is why I keep the reader's CONDITIONAL verdict unchanged rather than rejecting the paper. If the proposed λ/threshold test shows support size is λ-dependent or threshold-dependent, the authors should either temper the dimensional-discovery claim or explicitly reframe the support count as a regularization-induced proxy. I partially agree with the reader's weakest-assumption statement: the low-dimensional shared-support representation is indeed a load-bearing premise, but my concern is more specific, namely that the chosen estimator of dimension is not demonstrated to measure dimension independently of the regularizer that creates the sparsity.","tokens_in":14961,"tokens_out":12150,"duration_ms":136832,"concrete_test":"On the Study I 'both rotations and translations' series, use the released code to run DISCUS over a λ sweep (for example, 1e-3 to 1e1) and record the support count of the learned z_t under a pre-specified nonzero threshold (for example, normalized amplitude greater than 1e-3) across at least 50 random initializations. Independently estimate the dimension of the noiseless reference series with PCA or a maximum-likelihood intrinsic-dimension estimator. If the recovered support varies with λ or with the threshold rather than matching the independent dimension estimate, the Section 2.2 claim that DISCUS discovers the intrinsic manifold dimensionality is not supported; the reconstruction-quality claims should then be evaluated separately from the dimensional-discovery claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.2 states that 'the number of non-zero entries in bz_t determines the dimensionality of the underlying manifold.' But Eq. 3 directly penalizes the support of z(1:T) via the ℓ2,1 term; with λ>0 tuned on fully sampled data, the optimizer is actively incentivized to zero out rows, so finding few nonzero entries is partly a consequence of the regularizer, not an independent measurement of the data. No threshold for 'nonzero' is reported in Sections 2.3 or 3.1, although Adam does not typically return exact zeros. The penalty also acts on spatial code pixels, not on intrinsic latent coordinates; because Gθ is a nonlinear U-Net with spatial mixing, one active pixel can generate many output degrees of freedom and several active pixels can be redundant, so support size is not an invariant of the image series. Study I is the only direct check and it is 8/10 for the two-dimensional series, with the paper itself noting that the two active entries did not disentangle rotations from translations. This does not invalidate the reconstruction results, but it leaves the central 'manifold discovery' claim unsupported for real LGE data, where no independent ground-truth dimension is available.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes DISCUS, an unsupervised dynamic MRI reconstruction method that extends deep image prior by adding group sparsity to frame-specific code vectors (Eq. 3). A single U-Net maps one static code z0 and one dynamic code zt to each frame, and the ℓ2,1 penalty on z(1:T) is intended to force the dynamic codes to share a small support, whose size the authors equate with the intrinsic dimensionality of the image manifold. The method is evaluated in four studies: a Shepp-Logan phantom with known manifold dimension (Study I), simulated free-breathing LGE from digital phantoms (Study II), retrospectively undersampled patient LGE (Study III), and prospectively undersampled patient LGE with blinded expert scoring (Study IV). DISCUS is compared against CS, L+S, DIP, and SG-DIP. The authors report consistently better NMSE/SSIM and expert scores, and they release code and representative data.","tokens_in":15113,"tokens_out":3112,"duration_ms":33895,"significance":"If the results hold, DISCUS would be a practically useful unsupervised reconstruction method for dynamic MRI because it requires no fully sampled training data and no pre-specified manifold dimension. The paper has genuine strengths: four complementary studies, an ablation isolating the group-sparsity contribution, blinded expert evaluation on prospective data, and public code/data. However, the central conceptual claim—that the support size of the learned dynamic codes measures the true manifold dimensionality—is not established, because the objective itself penalizes support and no threshold for 'nonzero' is given. The reconstruction-quality comparisons are convincing within the chosen baseline set, but the absence of manifold-based baselines and the small prospective reader study limit the strength of the broader claims. The manuscript is technically sound enough to merit revision, but the central claim needs reframing or additional evidence.","major_comments":[{"comment":"The statement that 'the number of non-zero entries in bz_t determines the dimensionality of the underlying manifold' is not supported as a discovery claim. The objective in Eq. (3) directly penalizes the temporal support of z(1:T) through the ℓ2,1 term, so finding few active entries is partly a regularization outcome, not an independent measurement. Moreover, Adam does not return exact zeros, yet no threshold for 'nonzero' is specified anywhere in Sections 2.3 or 3.1. Because Gθ is a nonlinear U-Net with spatial mixing, the support size in code space is not invariant to reparameterization: one active code pixel can affect many output degrees of freedom, and multiple active pixels can be redundant. Study I only achieves 8/10 correct dimensionality for the two-dimensional manifold, and the paper itself notes that the two active entries did not disentangle rotation from translation. I recommend reframing the contribution as 'DISCUS imposes a low-dimensional shared-support representation' rather than 'DISCUS discovers the manifold dimension,' and, if the discovery claim is retained, providing a precise zero-threshold definition, an invariance analysis, and a validation on real LGE data with an independent dimension estimate.","section":"Section 2.2, Eq. (3), Section 3.1"},{"comment":"The paper positions DISCUS against manifold-based dynamic DIP methods such as those of Yoo et al. and Gen-SToRM, and it claims superior performance, but no manifold-based baseline (e.g., time-dependent DIP, Gen-SToRM, DEBLUR, or MoCo-SToRM) is included in the comparisons. The current baselines (CS, L+S, DIP, SG-DIP) are reasonable but do not test the specific advantage DISCUS claims over methods that explicitly model a low-dimensional manifold. I ask the authors to either add at least one manifold-based baseline to the numerical comparisons or soften the comparative claims so that they are restricted to the evaluated methods.","section":"Section 2.8 and Section 3 (Studies II-IV)"},{"comment":"The prospective reader study is the only clinical evaluation, but it involves only eight patients. The average scores and 'best image count' are reported without inter-reader agreement statistics, and it is not clear whether the counts in Table 5 are summed over the two readers or represent consensus. Given that the average score advantage of DISCUS over L+S is small (4.63 vs 4.5) and the authors attribute the narrowed separation to MoCo, the evidence for a clinical advantage would be strengthened by per-reader scores, agreement measures (e.g., Cohen's kappa), and a clearer description of the scoring procedure.","section":"Section 2.6 and Table 5 (Study IV)"},{"comment":"The free parameters (λ, learning rate, iterations, and the dynamic-code channel count k) are tuned on an additional fully sampled retrospective dataset, but no sensitivity analysis is reported. Since λ directly controls the sparsity of the dynamic codes and thus the claimed manifold dimension, the manuscript should report the tuned values, the range over which performance is stable, and whether the same values are used for the prospective Study IV data. Without this, it is hard to assess whether the reported advantages are robust to parameter choice.","section":"Section 2.8"}],"minor_comments":[{"comment":"The text says DISCUS is tested at 'four different acceleration rates, i.e., R = 2, 3, 4, and 5,' but Table 2 also reports R = 6; the sentence and table should be made consistent.","section":"Section 3.2"},{"comment":"In the ablation study, the description says R = 4, but Table 3 does not explicitly repeat the acceleration rate in the caption; please state it clearly to avoid ambiguity.","section":"Section 2.4 / Table 3"},{"comment":"The phrase 'acceleration rate of R = 1 was enabled by lower spatial resolutions and longer temporal footprints' is confusing because R = 1 usually denotes no undersampling; please rephrase to clarify that this is a fully sampled reference acquisition with reduced resolution.","section":"Section 2.5"},{"comment":"There are several typographical errors, including 'dimensionailty', 'NSME', 'Undersampling' in Section 2.5, and 'not pre-defined' in Section 2.2; a copyedit pass would improve readability.","section":"Throughout"},{"comment":"The notation z_t[n] is used for the nth element of the dynamic code, but the paper does not define how the spatial index n is mapped to the 2D code grid; please specify the reshaping explicitly.","section":"Section 2.2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is likely to be of interest to the journal if the authors can address the circularity in the manifold-discovery claim and strengthen the clinical evidence. The reconstruction results are encouraging, and the code release is a significant asset. My main concern is that the central novelty—'discovering' the manifold dimension from the support of learned codes—is not currently established because the regularizer manufactures sparsity and no threshold or invariance analysis is provided. This can probably be fixed by reframing the claim and softening the language, but it is load-bearing for the paper's framing."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: DISCUS is a genuinely useful extension of deep image prior for dynamic MRI, and the paper convincingly shows the reconstruction works in simulation and on patients. The stronger claim, that it discovers the true manifold dimension, is not actually established.\n\nWhat's new: applying a group-sparsity (ℓ2,1) penalty to per-frame code vectors in a DIP network, so you don't need to pre-specify manifold dimension or assume temporal smoothness. That's a real extension of time-dependent DIP and Gen-SToRM, and it matters for single-shot LGE where frames aren't temporally ordered. The validation is above average for the subfield: four studies, multiple accelerations, ablations, blinded expert scoring of prospectively undersampled data, and code/data release. The consistent NMSE/SSIM margins over CS, L+S, DIP, and SG-DIP are believable.\n\nThe soft spot is the manifold-discovery narrative. The ℓ2,1 penalty is what creates the sparsity, so counting nonzero entries in the learned code is partly measuring the regularizer, not the data. The paper never gives the threshold used to call an entry nonzero, and Adam doesn't produce exact zeros, so the count is sensitive to that choice. Study I is the only direct check: 20/20 for one-dimensional series but only 8/10 for the two-dimensional one, and even the successful cases didn't disentangle rotation from translation. The authors acknowledge the latter, but the 'discovers manifold dimensionality' claim is still oversold. This doesn't undercut the reconstruction results—the ablation against DGS shows group sparsity is doing real work—but it should be reframed as 'empirically effective sparsity regularization' rather than dimensionality estimation.\n\nTwo more soft spots, both minor for a methods paper: the most relevant manifold-based baselines (time-dependent DIP and Gen-SToRM) are cited but not benchmarked, which weakens the positioning; and Study IV uses only eight patients and two readers, with no inter-reader agreement statistics. Hyperparameters were tuned on a fully sampled validation set; the text says it came from the retrospective study but doesn't specify whether it includes the same patients.\n\nBottom line: the core method looks sound and reproducible, and the reconstruction improvement is credible. The paper deserves a serious referee, but the authors should either add the missing baselines or soften the manifold-discovery language. I'd send it to review expecting revision rather than desk-reject.","headline":"DISCUS is a solid, practically useful extension of DIP for dynamic MRI, but the manifold-discovery claim is not supported by the evidence.","tokens_in":15732,"tokens_out":1896,"would_cite":true,"duration_ms":18905,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"DISCUS: one untrained U-Net with group-sparse dynamic codes reconstructs free-breathing cardiac MRI without fully sampled training data, and the number of nonzero code entries reports the data's manifold dimension.","keywords":["unsupervised MRI reconstruction","deep image prior","group sparsity","manifold learning","late gadolinium enhancement","dynamic MRI","single-shot cardiac imaging","structured sparsity"],"falsifier":"Run DISCUS on a digital phantom with a known, larger number of independent motion modes, say five local deformations with disjoint spatial supports, and compare the post-training support count with the true number across ten random restarts; the central claim would fail if the method regularly undercounts or overcounts, because the shared-support representation then cannot capture the true dynamics. A second check uses the paper's own two-motion phantom, where two of ten restarts estimated three dimensions, and asks whether those wrong-dimension runs also produce visibly incorrect reconstructions.","tokens_in":14652,"feed_emoji":"🧲","tokens_out":10213,"duration_ms":90556,"temperature":0.7,"pith_summary":"This paper proposes DISCUS, an unsupervised method for reconstructing dynamic MRI series that does not need fully sampled k-space data for training. The central claim is that a single U-Net, fed one static code vector and one per-frame dynamic code vector, can generate every frame of a free-breathing late gadolinium enhancement (LGE) series, provided the dynamic codes are penalized with group sparsity. That penalty makes the nonzero entries of the learned codes shared across frames, so the number of surviving entries reports the true dimensionality of the image manifold without the user having to preset it. The paper reports that DISCUS outperforms compressed sensing, low-rank plus sparse, deep image prior, and self-guided deep image prior on simulated phantoms, simulated LGE series, retrospectively undersampled patient data, and prospectively undersampled patient data scored by expert readers. If the claim holds, dynamic MRI reconstruction becomes feasible in settings where fully sampled references do not exist and the number of motion and contrast degrees of freedom is unknown.","feed_headline":"Untrained U-Net reconstructs cardiac MRI without training data","feed_subtitle":"Group sparsity on per-frame codes finds the true motion dimension, beating CS and DIP on LGE scans.","key_machinery":"The load-bearing mechanism is the hybrid $\\ell_2$-$\\ell_1$ group-sparsity regularizer applied to the dynamic code vectors. A U-Net $G_\\theta$ maps the concatenation of a static code $z_0$ (three channels in the implementation) and a single-channel dynamic code $z_t$ to an estimate of frame $x_t$; the regularizer computes $\\|z_{(1:T)}\\|_{2,1} = \\sum_{n=1}^{N} \\sqrt{\\sum_{t=1}^{T} z_t[n]^2}$, which penalizes the temporal energy of each pixel and forces the nonzero entries of $z_t$ to occupy the same positions across all frames. Counting those surviving positions after training gives the dimension of the image manifold, and the values of the surviving entries encode frame-to-frame variation. This distinguishes DISCUS from plain deep image prior, which has no code sparsity and is prone to overfitting, and from manifold methods that fix the dimension in advance or enforce temporal smoothness.","core_discovery":"On the paper's own terms, the discovery is that structured sparsity in latent space turns an untrained convolutional network into a manifold learner. DISCUS solves the objective in Equation (3): minimize $\\sum_{t}\\|A_t G_\\theta(z_0, z_t) - y_t\\|_2^2 + \\lambda \\|z_{(1:T)}\\|_{2,1}$ over the network weights $\\theta$, a static code $z_0$, and dynamic codes $z_t$, where the $\\ell_{2,1}$ term first takes per-pixel energy across time and then sums over pixels. Because this hybrid norm drives entire pixels' temporal trajectories to zero together, the learned dynamic codes share a common support; the number of nonzero entries in the trained $\\hat{z}_t$ is the discovered manifold dimension. The paper claims this support count matched the true dimension in the dynamic-phantom study (one for pure rotations, one for pure translations, and two for the combined motion in eight of ten runs) and that the resulting joint reconstruction outperformed compressed sensing, low-rank plus sparse, DIP, and SG-DIP in NMSE and SSIM across acceleration rates, with DISCUS being chosen as best most often in the prospective expert study. The method does not assume nearby frames are similar, which is why the authors position it for single-shot free-breathing LGE rather than for cine.","pith_inferences":["The paper's own dynamic-phantom result, where two of ten restarts found three nonzero entries instead of two, suggests that the discovered dimension should be treated as a distribution over restarts rather than a single exact number in practice.","Because the $\\ell_{2,1}$ penalty does not depend on the sampling trajectory, DISCUS should extend to radial or spiral single-shot acquisitions without changing the objective; the paper only tests Cartesian GRO masks.","A clinically useful extension would be to correlate the discovered manifold dimension with independent recordings of respiratory and cardiac motion; if the count tracks the number of physiological drivers, DISCUS could double as a motion-characterization tool."],"forward_implications":["Free-breathing single-shot LGE series can be reconstructed without fully sampled training data, without a preset manifold dimension, and without assuming temporally close frames look alike.","The ablation results imply that most of the quality gain comes from group sparsity: the no-group-sparsity variant trails DISCUS by more than 3 dB at every tested frame count.","Larger numbers of frames improve DISCUS quality, so the method exploits shared information across the whole series rather than reconstructing each frame independently.","The same framework is positioned to carry over to other single-shot dynamic applications such as first-pass perfusion and parametric mapping, where consecutive frames are not necessarily similar and fully sampled references are hard to obtain."],"supporting_citations":[{"why":"It supplies the deep image prior architecture and objective that DISCUS extends from a single image to a whole series.","marker":"[14]"},{"why":"It is the self-guided DIP baseline that DISCUS is compared against and aims to improve on for noisy data.","marker":"[18]"},{"why":"It defines the time-dependent DIP baseline whose temporal-smoothness assumption DISCUS is designed to drop.","marker":"[21]"},{"why":"It is the manifold-learning baseline that presets the manifold dimension, the requirement DISCUS claims to remove.","marker":"[22]"},{"why":"It is the compressed-sensing sparsity baseline that DISCUS must beat in the NMSE and SSIM comparisons.","marker":"[5]"},{"why":"It is the low-rank-plus-sparse joint reconstruction used as a competitor and as the ablation comparison.","marker":"[6]"},{"why":"It introduces the grouped-variable sparsity norm that becomes the structured-sparsity penalty in DISCUS.","marker":"[31]"},{"why":"It provides the realistic MRXCAT digital cardiac phantoms used in the simulation study.","marker":"[34]"},{"why":"It defines the golden-ratio-offset Cartesian sampling masks used for undersampling in all studies.","marker":"[36]"},{"why":"It is the ESPIRiT coil-sensitivity estimation used to preprocess measured patient k-space data.","marker":"[4]"}],"fun_headline_variants":["Structured sparsity turns untrained CNN into MRI manifold learner","No training data needed: DISCUS finds motion manifold for cardiac MRI","Untrained network with group sparsity recovers cardiac MRI better than CS and DIP","Manifold discovery via group sparsity: unsupervised MRI recovery","Group sparsity lets untrained CNN find cardiac MRI motion manifold"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that every frame-to-frame change in the image series can be represented by a small set of code entries whose positions are shared across frames; if real motion or contrast changes need many independent degrees of freedom, the group-sparsity penalty will either erase them or lock onto the wrong support.","fun_headline_variants_meta":{"raw":{"variants":["Structured sparsity turns untrained CNN into MRI manifold learner","No training data needed: DISCUS finds motion manifold for cardiac MRI","Untrained network with group sparsity recovers cardiac MRI better than CS and DIP","Manifold discovery via group sparsity: unsupervised MRI recovery","Group sparsity lets untrained CNN find cardiac MRI motion manifold"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000912,"raw_usage":{"total_tokens":3981,"prompt_tokens":1068,"completion_tokens":2913,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":684,"completion_tokens_details":{"reasoning_tokens":2831}},"tokens_in":684,"tokens_out":2913,"duration_ms":18643,"temperature":1.0,"reasoning_tokens":2831,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:29:12.903733+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run DISCUS on a digital phantom with a known, larger number of independent motion modes, say five local deformations with disjoint spatial supports, and compare the post-training support count with the true number across ten random restarts; the central claim would fail if the method regularly undercounts or overcounts, because the shared-support representation then cannot capture the true dynamics. A second check uses the paper's own two-motion phantom, where two of ten restarts estimated three dimensions, and asks whether those wrong-dimension runs also produce visibly incorrect reconstructions.","supporting_citations":[{"cited_title":"Deep image prior","cited_arxiv_id":null,"evidence_quote":"It supplies the deep image prior architecture and objective that DISCUS extends from a single image to a whole series."},{"cited_title":"Robust Self-Guided Deep Image Prior","cited_arxiv_id":null,"evidence_quote":"It is the self-guided DIP baseline that DISCUS is compared against and aims to improve on for noisy data."},{"cited_title":"Time-dependent deep image prior for dynamic MRI","cited_arxiv_id":null,"evidence_quote":"It defines the time-dependent DIP baseline whose temporal-smoothness assumption DISCUS is designed to drop."},{"cited_title":"Dynamic imaging using a deep generative SToRM (Gen-SToRM) model","cited_arxiv_id":null,"evidence_quote":"It is the manifold-learning baseline that presets the manifold dimension, the requirement DISCUS claims to remove."},{"cited_title":"Sparse MRI: The application of compressed sensing for rapid MR imaging","cited_arxiv_id":null,"evidence_quote":"It is the compressed-sensing sparsity baseline that DISCUS must beat in the NMSE and SSIM comparisons."},{"cited_title":"Low-rank plus sparse matrix decomposition for acceler- ated dynamic MRI with separation of back- ground and dynamic components","cited_arxiv_id":null,"evidence_quote":"It is the low-rank-plus-sparse joint reconstruction used as a competitor and as the ablation comparison."},{"cited_title":"Model selection and esti- mation in regression with grouped variables","cited_arxiv_id":null,"evidence_quote":"It introduces the grouped-variable sparsity norm that becomes the structured-sparsity penalty in DISCUS."},{"cited_title":"MRXCAT: Realistic numerical phantoms for cardiovascular magnetic resonance","cited_arxiv_id":null,"evidence_quote":"It provides the realistic MRXCAT digital cardiac phantoms used in the simulation study."},{"cited_title":"ESPIRiT—an eigenvalue approach to autocalibrating parallel MRI: where SENSE meets GRAPPA","cited_arxiv_id":null,"evidence_quote":"It is the ESPIRiT coil-sensitivity estimation used to preprocess measured patient k-space data."}],"review_version":1}