{"id":"6eea7580-f734-4c44-927a-1f7a29fb34cf","arxiv_id":"2501.18219","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Microlocally inspired mask-shaped filters let ΨDONet match or slightly improve limited- and sparse-angle CT reconstructions with far fewer learnable parameters.","lead":"This paper revisits ΨDONet, a learned iterative reconstruction network for incomplete-data CT, adding a microlocal analysis and proposing new masked filter shapes. The new filters use far fewer learnable parameters and match or slightly improve reconstruction quality on simulated limited-angle and sparse-angle scans.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Numerical parity claim is not statistically supported: reported PSNR/SSIM differences are small and no seeds or error bars are given; the theoretical 'prevention' claim in §4.3 is also only conditional.","rationale":"I agree with the reader that the Parseval-frame assumption in Section 4.1 is a genuine gap between the continuous formulation and the discrete Haar implementation, and it deserves attention. However, I do not think it is the most load-bearing issue for the paper's central claim. The paper's headline practical contribution is numerical: masked filters with fewer parameters give essentially equal or slightly better PSNR/SSIM. That claim rests on single-run comparisons with no variance information. The reported differences—up to a few tenths of a dB—are exactly the magnitude one expects from random initialization and training noise in a deep unrolled network, especially with only 15 epochs. The absence of code and error bars makes it impossible to distinguish a true parity result from a fortuitous run. This is a concrete, testable weakness, and it directly controls whether the paper's main advertised benefit exists. The theoretical 'prevention of streak artifacts' claim is also weaker than advertised: Section 4.3 derives a representational identity and then says the learned filters 'might' smooth the kernel, while the abstract/conclusion assert that ΨDONet can prevent streak artifacts. The paper's own Figure 6 shows residual partial streaks, so the empirical evidence does not support the strong reading. These issues do not make the paper fundamentally wrong; they make the central claims conditional on reproducibility and on a more careful statement of what is proved. Hence the reader's CONDITIONAL verdict should stand, with the concrete repeated-seed experiment above as the natural acceptance condition.","tokens_in":17285,"tokens_out":12378,"duration_ms":132195,"concrete_test":"Retrain Ψo, Ψbow^1, Ψx^1, and Ψspa^1 for each of the three geometries in Tables 1–3 using 5 independent random seeds and report mean ± std PSNR/SSIM. If the best masked variant's gain over Ψo is smaller than the pooled standard error, the parity claim is not established; if the gain exceeds the standard error consistently, the claim survives. As a secondary check, inspect a trained model's effective subband kernels κ_A^{ι,ι'} + eκ^{ι,ι'} and measure whether the jump across the missing-wedge boundary directions is actually reduced relative to κ_A^{ι,ι'}; this would test whether the §4.3 smoothing mechanism is what training produces.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's strongest practical claim is that the masked-filter variants (Ψbow, Ψx, Ψspa) preserve or slightly improve reconstruction quality over the full-square Ψo while using considerably fewer learnable parameters (Section 5, Tables 1–3). The reported advantages are small: +0.18 dB and +0.32 dB PSNR for the best Ψx variants in Tables 1–2, and +0.03/+0.16 dB for Ψspa in Table 3. No error bars, no multiple-seed experiments, and no runnable code are provided; the repository is explicitly withheld until acceptance. For a 10-block unrolled network trained with Adam, these gaps are plausibly within run-to-run variance. If the parity claim is not reproducible across seeds, the practical contribution—equal quality at a lower parameter count—is unsupported, because every reported advantage could be initialization noise. Separately, Section 4.3 proves only the convolutional representation (10) and states that the learned filters 'might' smooth the kernel; it does not prove that training finds such a smoothing correction. The conclusion's 'can prevent' is stronger than what is shown, and Figure 6 even reports residual partial streak artifacts for Ψspa.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper revisits the ΨDONet architecture for limited-angle and sparse-angle tomography. It introduces a continuous wavelet-domain formulation of the unrolled ISTA scheme, uses microlocal analysis (following [3]) to argue that soft-thresholding can introduce new edges and that learned convolutional corrections can prevent streak artifacts by smoothing the kernel of R_A^* R_A, and proposes three masked-filter variants (Ψbow, Ψx, Ψspa) whose supports are informed by the visible cone and the missing-wedge boundary. Numerical experiments on synthetic ellipse data report that these variants achieve nearly identical or slightly better PSNR/SSIM than the original full-square ΨDONet while using considerably fewer learnable parameters, and provide a proof-of-concept for sparse-angle data.","tokens_in":17550,"tokens_out":3207,"duration_ms":31950,"significance":"If the claims are supported, the paper makes a useful contribution: it gives a theoretically motivated way to reduce the parameter count of ΨDONet without sacrificing reconstruction quality, and it extends the architecture to sparse-angle tomography. The continuous formulation and the convolutional-kernel representation in Eq. (10) are valuable steps, and the paper correctly credits the tools imported from [3]. However, the central numerical claim is not statistically established: the reported improvements are small (0.03–0.32 dB) and no error bars, seeds, or multiple-run comparisons are given. The theoretical claim of 'prevention' of streak artifacts is only conditional in Section 4.3, and the Parseval-frame assumption used in Section 4.1 is not verified for the Haar wavelet system actually implemented. These gaps are load-bearing for the paper's main conclusions.","major_comments":[{"comment":"The central numerical claim is that the masked-filter variants preserve or slightly improve reconstruction quality, but the reported differences are very small (e.g., +0.18 dB and +0.32 dB PSNR for Ψx in Tables 1 and 2, +0.03 and +0.16 dB for Ψspa in Table 3) and no error bars, number of training runs, random seeds, or statistical significance tests are provided. With a single run of a 10-block unrolled network trained by Adam, these gaps are plausibly within run-to-run variance. To support the parity/improvement claim, the authors should report multiple-seed experiments (at least 3–5 runs) with mean and standard deviation, or provide per-image test-set distributions and a paired test. Without this, the practical contribution of equal quality at lower parameter count is not established.","section":"Section 5, Tables 1–3"},{"comment":"The theoretical argument in Section 4.3 only proves the convolutional representation of W R_A^* R_A W^* + Λ_k and then states that the learned filters 'might' smooth the discontinuities of κ_A. It does not prove that training finds such a smoothing correction, nor does it characterize the trained filters. The conclusion in Section 6, however, states that ΨDONet 'can prevent' streak artifacts from appearing, which is stronger than what is shown. Figure 6 even reports residual partial streak artifacts for the Ψspa reconstruction in the 6-angle case. The authors should either soften the claim to 'reduce' or 'dampen' artifacts, or provide direct evidence (e.g., inspecting the learned filters or the effective kernel) that the trained correction indeed smooths κ_A.","section":"Section 4.3, Eq. (10), and Section 6"},{"comment":"The continuous formulation in Section 4.1 assumes that the translation-invariant, finitely scaled wavelet frame is Parseval, so that W^* acts as a reconstruction operator and Eq. (8) faithfully represents the discrete network. The numerical experiments, however, use Haar wavelets with scales J0=4 and J=7 (Section 5), a setting for which the Parseval property is not established. If the frame is not Parseval, the microlocal analysis in Sections 4.2 and 4.3 describes a different operator from the one actually trained and evaluated. The authors should either prove the Parseval property for the implemented wavelet system (including the finite-scale truncation) or explicitly state this as an idealization that limits the scope of the theoretical conclusions.","section":"Section 4.1, Eq. (8), and Section 5"}],"minor_comments":[{"comment":"The caption contains a typo: 'when only limited data are are available' should be 'when only limited data are available'.","section":"Section 2.2, Figure 1 caption"},{"comment":"The phrase 'a new continuos formulations' should be 'a new continuous formulation'.","section":"Section 4, opening paragraph"},{"comment":"The sentence 'We report the average PSNR and SSIM in Table 1' refers to the second limited-angle experiment but should refer to Table 2, not Table 1.","section":"Section 5.1, text after Table 2"},{"comment":"The metric is referred to as 'structured similarity index'; the standard name is 'structural similarity index' (SSIM).","section":"Section 5, first paragraph"},{"comment":"There is a typo in 'different visisble wedges'; it should be 'different visible wedges'.","section":"Section 6, Conclusions"},{"comment":"The repository is stated to be made available only upon acceptance. For a paper whose main contribution is numerical, it would strengthen reproducibility to provide the code or at least detailed training and evaluation scripts during the review process.","section":"Section 5"}],"recommendation":"major_revision","confidential_remarks":"The paper is heavily based on the authors' own prior work [9] and on [3]; the novelty is incremental but potentially useful if the numerical claims are properly supported. The biggest risk is that the reported performance gains are within training noise; I would recommend requiring multiple-seed experiments before acceptance. Also, the theoretical 'prevention' claim should be aligned with the actual conditional result in Section 4.3. The withheld code is a concern for reproducibility and should be made available to reviewers if the journal's policy permits."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid, honest follow-up to the ΨDONet line, with two genuinely new things — the masked filter geometries (bowtie, cross, sparse-angle) and the wavelet-domain kernel-smoothing argument for why a learned correction can suppress streak artifacts. The sparse-angle proof-of-concept is also new. I believe the paper deserves a serious referee, but the numerical parity claim is not yet nailed down and the theory is a bit oversold.\n\nWhat it does well: the masked filters are a clean, microlocally motivated way to cut parameters, and Tables 1–3 show the quality holds up (or slightly improves) across limited-angle and sparse-angle settings. The authors are transparent that the sparse-angle part is a proof of concept. Section 4.3's observation that the learned filters act directly on the discontinuous kernels κ_{A,ι,ι′} in the wavelet domain is a nice formalization, and restricting the analysis to singular support rather than wavefront is an honest choice given that wavelets do not resolve direction.\n\nWhere I'd push back. First, the numbers. All PSNR/SSIM values are averages over a test set with no error bars, no seeds, and no code. Differences of 0.1–0.3 dB between the original and masked variants are exactly the sort that can flip with initialization. Without at least a few seeds or per-image distributions, the central claim — same quality at lower parameter count — is plausible but unproven. Second, the theoretical \"prevention\" claim in the abstract and conclusion is stronger than Section 4.3: the text says learned filters \"might\" smooth the kernel, and Figure 6 still shows partial streaks for Ψspa. The math shows it is possible in principle, not that training finds such filters. Third, the continuous formulation in Section 4.1 assumes the finitely scaled, continuously translated wavelet frame is Parseval. That is not established for the Haar wavelets with J0=4 to J=7 actually used, and the discrete network uses a critically sampled orthogonal transform, not the continuous frame. So the microlocal analysis may be describing a slightly different operator. This is a real gap, though probably patchable.\n\nAlso minor: parameter counts for the masked variants are never reported explicitly, and there are no external baselines, so the practical significance is bounded. The circularity burden is real but not damning — building on one's own architecture and importing [3, Thm 4.11] is fine, and the mask designs are new.\n\nBottom line: this is a useful, readable paper for the learned-tomography audience. I'd send it to review, with requests for code, seeds/error bars, explicit parameter counts, and a toned-down conclusion. The central idea deserves to be published; it just needs the evidence to match the language.","headline":"Honest, useful extension of ΨDONet with clever masked filters and a plausible microlocal story; the parity claim still needs error bars and code, and the \"prevention\" wording outruns the math.","tokens_in":18100,"tokens_out":3727,"would_cite":true,"duration_ms":32857,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["65R10","68T07"],"pacs":[],"model":"deepseek-v4-flash","headline":"Masked filters restricted to the visible cone match or slightly beat the original ΨDONet's reconstruction quality with far fewer learnable parameters.","keywords":["limited-angle tomography","sparse-angle tomography","microlocal analysis","wavelet frames","unrolled optimization","pseudodifferential operators","streak artifacts","computed tomography"],"falsifier":"Compute the frame bounds (or their ratio) of the translation-invariant Haar frame with scales $J_0=4$ and $J=7$ used in Section 5; if the upper and lower bounds are far apart, the continuous kernel-smoothing mechanism analyzed in Section 4.3 does not describe the implemented network. A second check would be to retrain the masked variants on a wavelet frame certified to be Parseval and see whether the masked filters still match the full-square filter quality; if they do not, the proposed mechanism is not the source of the numerical result.","tokens_in":17074,"feed_emoji":"🩻","tokens_out":8915,"duration_ms":79929,"temperature":0.7,"pith_summary":"This paper revisits ΨDONet, a neural network built by unrolling iterative soft-thresholding for tomographic reconstruction, and gives a fuller microlocal account of what that network does: it can introduce edges that are invisible in the incomplete sinogram, and it can prevent streak artifacts rather than only dampening them, by smoothing the kernel of the incomplete-data backprojection operator. The paper's numerical claim is that the learnable filters can be masked down to the cone of visible directions (Ψbow) or to wedges along the boundary of the missing wedge (Ψx, Ψspa) with no loss, and sometimes a small gain, in PSNR and SSIM on limited-angle and sparse-angle test images, at considerably lower parameter counts. This matters because it shows that theoretical knowledge of where artifacts come from can be converted directly into cheaper learned reconstruction networks of equal quality.","feed_headline":"Masked filters match full ΨDONet with fewer parameters","feed_subtitle":"Three filter shapes inspired by streak-artifact geometry preserve limited- and sparse-angle CT reconstruction quality.","key_machinery":"The carrying identity is the wavelet-domain representation $[W R_A^* R_A W^* w + \\Lambda_k w]_\\iota = \\sum_{\\iota'} (\\kappa^{\\iota,\\iota'}_A + \\tilde\\kappa^{\\iota,\\iota'}_k) * w_{\\iota'}$, where $\\kappa^{\\iota,\\iota'}_A$ are the wavelet subband kernels of $R_A^* R_A$ and $\\tilde\\kappa^{\\iota,\\iota'}_k$ are the learned filter functions. The argument works by comparing the full normal operator, whose kernel $1/\\|x-y\\|$ identifies it as a pseudodifferential operator, with the incomplete-data kernel $\\kappa_A(x-y) = \\|x-y\\|^{-1}\\chi^c_A(x-y)$, whose jumps along the cone directions are the source of streak artifacts. The three masked filter geometries (bowtie in the visible cone, cross along the boundary directions, and sparse along the sampled directions) place learnable parameters exactly where kernel jumps occur, implementing the smoothing with minimal parameter count.","core_discovery":"The central claim is that ΨDONet's correction term can be understood, in a continuous semi-discrete wavelet formulation, as adding learned convolutional filters to the wavelet-domain kernels of the incomplete-data normal operator $R_A^* R_A$; when those filters smooth the discontinuities introduced by the truncation cone $\\chi^c_A$ inside the kernel $\\kappa_A$, the corrected operator behaves like a pseudodifferential operator and streak singularities are removed at their source rather than only reduced in amplitude. A second claim is that the pointwise soft-thresholding at each wavelet subband creates new singularities, which explains how invisible edges may reappear, although the analysis cannot predict where they will appear. The numerical consequence is that filters only need to be learned where the kernel or its jumps live: bowtie-shaped supports inside the visible cone for limited-angle tomography, and thin wedges along the directions $\\partial A$ for both limited- and sparse-angle tomography. Reported experiments on synthetic ellipse data show these masked variants preserve or slightly improve PSNR and SSIM relative to the original square filters while using far fewer learnable parameters.","pith_inferences":["An untested extension, natural from the same reasoning, is to apply the mask-construction principle to other limited-data geometries such as exterior or region-of-interest tomography, where the artifact directions are likewise determined by the boundary of the available angular set.","The parameter savings could be reinvested in larger filter radii or more unrolled layers at a fixed total parameter count, which may improve fidelity in settings where the ten-layer architecture is the bottleneck.","Because the present analysis tracks only singular support, not direction, extending the architecture to directional dictionaries such as shearlets or curvelets would be the natural route to predicting which invisible edges are recovered; the paper itself notes that this would require redesigning the network.","The reported gains are established on synthetic ellipse images only; whether the same parameter reduction preserves quality on real experimental computed-tomography measurements remains an open empirical question."],"forward_implications":["The masked variants cut the number of learnable parameters substantially while keeping PSNR and SSIM unchanged, so limited-angle and sparse-angle ΨDONet can be trained and deployed at lower cost without sacrificing reconstruction quality.","In the 120-degree missing-wedge experiment the masked variants slightly outperform the original square filters, and the reported images show better preservation of small, low-contrast features.","For 6-angle and 12-angle sparse-angle data, the Ψspa filters do not worsen the metrics and, in the reported images, reduce the magnitude of partial streak artifacts compared with the square-filter baseline.","The theoretical analysis implies that the soft-thresholding nonlinearity can introduce singularities not present in the data, so some invisible edges may be recovered, but the current architecture cannot predict or control where those edges appear.","If the learned filters really smooth the kernel discontinuities as argued, ΨDONet prevents streak artifacts from forming in the first place, rather than only attenuating them after they appear."],"supporting_citations":[{"why":"Supplies the original ΨDONet architecture, its pseudodifferential-correction rationale, the wavelet-domain convolution representation, and the ellipse training and test datasets reused here.","marker":"[9]"},{"why":"Provides the microlocal analysis of ReLU and Nemytskii operators used in Proposition 3 and Corollary 4 to show that soft-thresholding can introduce new singularities.","marker":"[3]"},{"why":"Establishes the kernel form $\\kappa_A = \\|x-y\\|^{-1}\\chi^c_A$ and the result that streak artifacts arise from discontinuities at $\\partial A$, which motivates the masked filter supports.","marker":"[8]"},{"why":"Supplies the visible-versus-invisible singularity principle used to decide which edges can be recovered from an incomplete sinogram.","marker":"[33]"},{"why":"Gives the ISTA iteration and its convergence theory, the scheme whose unrolling defines ΨDONet.","marker":"[13]"},{"why":"Provides the translation-invariant wavelet frame construction and the Parseval-frame conditions on which the continuous formulation rests.","marker":"[30]"}],"fun_headline_variants":["Streak-aware filters slash parameters in ΨDONet","Microlocal filters shrink ΨDONet without losing quality","Bowtie filters cut ΨDONet parameters, keep CT quality","Learned filters target artifacts to slim ΨDONet","ΨDONet slims down with streak-geometry filters"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The continuous analysis assumes the wavelet dictionary is Parseval, meaning that reconstructing from wavelet coefficients is exact, but the Haar implementation with scales $J_0=4$ to $J=7$ used in the experiments is not shown to satisfy this, so the operator analyzed may differ from the operator actually trained.","fun_headline_variants_meta":{"raw":{"variants":["Streak-aware filters slash parameters in ΨDONet","Microlocal filters shrink ΨDONet without losing quality","Bowtie filters cut ΨDONet parameters, keep CT quality","Learned filters target artifacts to slim ΨDONet","ΨDONet slims down with streak-geometry filters"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000238,"raw_usage":{"total_tokens":1480,"prompt_tokens":882,"completion_tokens":598,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":498,"completion_tokens_details":{"reasoning_tokens":512}},"tokens_in":498,"tokens_out":598,"duration_ms":5359,"temperature":1.0,"reasoning_tokens":512,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T00:15:55.020309+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the frame bounds (or their ratio) of the translation-invariant Haar frame with scales $J_0=4$ and $J=7$ used in Section 5; if the upper and lower bounds are far apart, the continuous kernel-smoothing mechanism analyzed in Section 4.3 does not describe the implemented network. A second check would be to retrain the masked variants on a wavelet frame certified to be Parseval and see whether the masked filters still match the full-square filter quality; if they do not, the proposed mechanism is not the source of the numerical result.","supporting_citations":[{"cited_title":"Deep neural networks for inverse problems with pseudodifferential operators: An application to limited-angle tomography","cited_arxiv_id":null,"evidence_quote":"Supplies the original ΨDONet architecture, its pseudodifferential-correction rationale, the wavelet-domain convolution representation, and the ellipse training and test datasets reused here."},{"cited_title":"Deep microlocal reconstruc- tion for limited-angle tomography","cited_arxiv_id":null,"evidence_quote":"Provides the microlocal analysis of ReLU and Nemytskii operators used in Proposition 3 and Corollary 4 to show that soft-thresholding can introduce new singularities."},{"cited_title":"Analyzing reconstruction artifacts from arbitrary incomplete X-ray CT data","cited_arxiv_id":null,"evidence_quote":"Establishes the kernel form $\\kappa_A = \\|x-y\\|^{-1}\\chi^c_A$ and the result that streak artifacts arise from discontinuities at $\\partial A$, which motivates the masked filter supports."},{"cited_title":"Artifacts and visible singularities in limited data X-ray tomography","cited_arxiv_id":null,"evidence_quote":"Supplies the visible-versus-invisible singularity principle used to decide which edges can be recovered from an incomplete sinogram."},{"cited_title":"An iterative thresholding algorithm for linear inverse problems with a sparsity constraint","cited_arxiv_id":null,"evidence_quote":"Gives the ISTA iteration and its convergence theory, the scheme whose unrolling defines ΨDONet."}],"review_version":1}