{"id":"931ce49b-0b1b-4aa2-ae87-d003f7f197c4","arxiv_id":"1908.04215","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A complete two-step numerical inversion for acousto-electric tomography reconstructs conductivity from simulated boundary data for coupling constants 1e-9 to 1e-7 Pa^-1 and noise up to 0.1%, with quality controlled by the coupling-to-noise ratio.","lead":"Ultrasound and electricity are combined on a computer to map the electrical conductivity inside a body from boundary measurements. This study shows the two-step reconstruction works in simulations across the coupling strengths and noise levels expected in medical applications, assuming the sound field inside is known.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Feasibility claim rests on exact interior acoustic fields p_j and a known constant eta; kernel errors in the ill-conditioned Step 1 are untested, so the demonstrated eta/delta tradeoff may not transfer.","rationale":"The reader's weakest_assumption identifies the same load-bearing concern I find: the entire first, ill-posed step depends on exact knowledge of the internal acoustic pressure and of a single constant coupling parameter. I agree with the CONDITIONAL verdict because the paper's own limitations section concedes these idealizations, and the numerical experiments never test them. I add one related observation: the regularization parameter in Step 1 is selected using the true power density H, so the reported reconstructions are optimistic even within the authors' own idealized setting. Neither point is a reason to reject the paper; the mathematical framework and the parameter study are valuable. But the central 'feasible for medical imaging' claim is stronger than the evidence when read strictly. The proposed test would show whether the demonstrated eta/delta tradeoff survives realistic kernel and parameter uncertainty. Since the reader already assigned CONDITIONAL, my verdict is unchanged.","tokens_in":12220,"tokens_out":2857,"duration_ms":33993,"concrete_test":"Re-run the Section 4 experiments with a parameter-choice rule that does not use the true H (e.g., L-curve or Morozov discrepancy), and corrupt the acoustic kernel by adding 1% spatially correlated error to p_j (or equivalently 1% uncertainty in c0 and source positions) and a +/-10% error in eta. Compare Figure 6 row 2 or 3 reconstructions against the current ones; if inclusion contrast or edge localization degrades substantially, the feasibility claim is not supported outside the exact-p/eta idealization.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that AET is feasible follows from a pipeline whose first and most ill-posed stage (2.3)-(2.12) takes p_j(x,t) and eta as exact, known inputs. The paper states this explicitly: c and S are 'fully known', eta is 'assumed throughout to be a known constant', and the conclusion lists 'accurate knowledge of the internal pressure field' as the main idealization. This is load-bearing because the kernel matrix K in (2.10) has exponentially decaying singular values (Fig. 4); small errors in w^k_{j,n} from transducer positioning, wave-speed uncertainty, or attenuation will be amplified before regularization. Moreover eta is tissue-dependent (cited values range from about 1e-9 Pa^-1 in saline to 4e-8 Pa^-1 in rabbit heart), so a single known eta is not a small detail. The reported noise study varies only electronic noise on g; it never perturbs p or eta. In addition, beta in (2.12) is chosen from the true-H error curve, which preselects the best possible regularization. Together these mean the numerical feasibility results are conditional on idealizations that are central to the ill-posed first step, not peripheral.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a complete two-step computational inversion framework for acousto-electric tomography (AET). In Step 1, the interior power density H is reconstructed from boundary voltage time series by solving the linear Fredholm system (2.3), discretized with Neumann eigenfunctions and regularized by a Sobolev-type penalty (2.12). In Step 2, the conductivity sigma is recovered from H by minimizing the L1-TV functional (2.13) via an iteratively reweighted linearization (2.14). The authors perform synthetic numerical experiments with physically motivated parameters (eta between 10^-9 and 10^-7 Pa^-1, noise levels between 0% and 0.1%) and report that AET is feasible for medical imaging, including a limited-angle setup. The paper also derives the boundary-to-power-density identity (2.1) and discusses the dependence of reconstruction quality on the ratio eta/delta.","tokens_in":12449,"tokens_out":5259,"duration_ms":50331,"significance":"If the feasibility claim holds, this is a valuable contribution: it is one of the few studies that deliberately models both steps of AET and examines the eta/delta tradeoff in a realistic parameter regime. The derivation of the boundary-to-power-density identity (2.1) is clean, and the numerical experiments are internally consistent. However, the study's strength is conditional: the forward and inverse models share the same exact acoustic fields and the same constant eta, and the Step-1 regularization parameter is selected with oracle knowledge of the true solution. These idealizations bear directly on the feasibility claim. The paper explicitly acknowledges them in the conclusion, but they are not tested or mitigated. The manuscript would be strengthened by quantitative error assessment and by experiments that perturb the acoustic field and the coupling parameter.","major_comments":[{"comment":"The first step assumes exact knowledge of the interior acoustic pressure field p_j(x,t_k) and the constant acousto-electric coupling eta. The kernel w^k_{j,n} in (2.7) and the linear system (2.11) require p_j as input, and the interpretation of I_{i,j} in (2.3) requires eta. The paper's own conclusion identifies 'accurate knowledge of the internal pressure field' as an idealization and notes that the assumption that eta is a known constant 'seems to be impractical.' Because the matrix K has exponentially decaying singular values (Fig. 4), errors in p_j or in eta will be amplified before regularization. The noise study in Section 3.2 perturbs only the boundary data g^k_{i,j}; it never perturbs p_j or eta. Thus the demonstrated eta/delta tradeoff may not transfer to a real instrument, and the central feasibility claim is not yet established under realistic uncertainty in the acoustic field.","section":"Section 2.1, Eqs. (2.3), (2.7), (2.11)"},{"comment":"The regularization parameter beta in (2.12) is chosen 'optimally by computing the regularization-error curve and picking the minimum error choice,' i.e., using the true power density H. This is an oracle selection that provides an upper bound on achievable quality. A practical feasibility study should test a data-driven selection rule (e.g., Morozov discrepancy principle or an L-curve criterion) or at least report sensitivity of the reconstructions to beta. Without this, the reported quality of Step 1, and hence Step 2, is likely optimistic.","section":"Section 4.1, Eq. (2.12)"},{"comment":"The assumption that eta is a known constant across the domain is inconsistent with the cited experimental values (eta about 4.1e-8 Pa^-1 in rabbit heart versus about 1e-9 Pa^-1 in saline), which suggest that eta is tissue-dependent. If eta varies spatially, the first-step equation (2.3) becomes I_{i,j}(t) = - Integral p_j(x,t) eta(x) H_i(x) dx, so the product eta H_i is what can be recovered, and separating eta from H would require additional information. The paper does not address this case, and the conclusion mentions it only in passing. This is a load-bearing gap for the claim of feasibility for medical imaging applications.","section":"Section 1, Eq. (1.3) and Section 3.1"},{"comment":"The conductivity reconstructions are assessed only visually; no quantitative error measures (e.g., relative L2 error, structural similarity, or contrast metrics) are reported. The central claim that the conductivity is 'well reconstructed' and the observed diagonal eta/delta pattern are supported only by qualitative inspection. Given that the paper's goal is to establish feasibility, quantitative assessment of the reconstructions is needed to substantiate the claim.","section":"Section 4.2, Figs. 6-8"}],"minor_comments":[{"comment":"The definition of the vector I_i is inconsistent: the last entry is written as I^{Nt}_{Nf,NS}, but since i is fixed, it should be I^{Nt}_{i,NS}, and the vector should lie in R^{NS Nt} rather than R^{Nf NS Nt} as printed.","section":"Section 2.1, Eq. (2.9)"},{"comment":"The expression 'hat H_i = min_{hat H in R^{N_phi}} ...' should read 'argmin' (or 'hat H_i = argmin'), since the right-hand side is a number and the left-hand side is a vector.","section":"Section 2.1, Eq. (2.12)"},{"comment":"The table caption contains a typo: 'Tabel' should be 'Table'.","section":"Table 1"},{"comment":"It would be helpful to state explicitly that the noise model does not perturb the acoustic field p or the coupling constant eta, since this is central to the interpretation of the numerical results.","section":"Section 3.2"},{"comment":"The abstract's statement that 'AET is indeed feasible for interesting applications' is stronger than what the experiments can support given the acknowledged idealizations; a more guarded phrasing would reflect the conditional nature of the results.","section":"Section 5 and Abstract"}],"recommendation":"major_revision","confidential_remarks":"The paper is mathematically sound and the numerical experiments are internally consistent, but the central feasibility claim is conditional on idealizations that are acknowledged in the conclusion and not tested in the experiments. The oracle choice of the Step-1 regularization parameter and the absence of quantitative reconstruction errors further weaken the claim. I believe the authors can address these concerns with additional experiments and revised conclusions, so this is a major revision rather than a rejection. The group has relevant prior work, and the topic is within the journal's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a careful numerical feasibility study of acousto-electric tomography, and the first I've seen that actually closes the loop: boundary currents and voltages in, conductivity out, through both steps of the reconstruction. What's genuinely new is the combination of a spectral inversion for the power density from boundary time series (Step 1) with the total-variation conductivity update from Adesokan et al. (Step 2), tested over realistic coupling constants (η = 1e-7 to 1e-9 Pa^-1) and noise levels (0% to 0.1%). They use k-Wave for the acoustic field and FEniCS for the electric problem, with parameters drawn from the tissue-impedance and EIT literature. The identities in Section 2 are clean, and the η/δ scaling argument in Section 3.2 is right: reconstructions at constant η/δ do look similar, which is a nice confirmation of the proposed tradeoff.\n\nThe soft spots are not hidden, but they temper the abstract's claim that AET is 'indeed feasible.' The first and most ill-posed step assumes the interior acoustic pressure field p_j and the coupling constant η are known exactly. As the authors admit in the conclusion, that is an idealization. With a kernel whose singular values decay exponentially (Fig. 4), small errors in p or η will be amplified before regularization helps. Their noise study perturbs only the boundary voltages, never p or η. Also, the regularization parameter β in (2.12) is chosen from the true-H error curve—an oracle choice that preselects the best possible reconstruction. The experiment is self-consistent, but it is not an external test of the feasibility claim.\n\nNone of this makes the paper worthless. The pipeline is a sensible baseline, the parameter scan is useful, and the limited-angle experiment matches the known boundary-near result. The honest reading is: AET looks feasible when you know p and η exactly and tune regularization with hindsight. Whether it works with realistic uncertainties is still open. Adding a discrepancy-principle choice for β and a sensitivity test with perturbed p and η would make the feasibility claim much stronger.\n\nI'd send this to peer review. It's a legitimate computational study with clear methodology and explicit limitations. I'd ask for those two additions, not because the current study is wrong, but because the central claim is about feasibility and the evidence is conditional on the most idealized part of the pipeline.","headline":"Solid, honest full-pipeline numerical feasibility study for AET; the 'feasible' claim is conditional on exact knowledge of the pressure field and oracle regularization, but the methodology and parameter scan earn referee time.","tokens_in":12983,"tokens_out":3505,"would_cite":true,"duration_ms":33332,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["35R30","65N21"],"pacs":[],"model":"deepseek-v4-flash","headline":"Acousto-electric tomography can reconstruct interior conductivity from boundary voltage time series, with quality set by the coupling-to-noise ratio.","keywords":["acousto-electric tomography","electrical impedance tomography","hybrid data tomography","coupled physics imaging","inverse problems","medical imaging","conductivity reconstruction","two-step inversion"],"falsifier":"Use the same two-step algorithm on synthetic data where the pressure field used for inversion differs from the true field by a few percent in amplitude or timing, or where $\\eta$ varies spatially; if the main phantom inclusions disappear at error levels consistent with clinical ultrasound, the feasibility claim as stated would fail.","tokens_in":12011,"feed_emoji":"🩺","tokens_out":8254,"duration_ms":80741,"temperature":0.7,"pith_summary":"The paper asks whether acousto-electric tomography (AET) can work under realistic physical parameters and answers yes, on the evidence of a complete two-step inversion pipeline tested on simulated data. Step one turns time-dependent boundary voltage measurements into the interior electric power density by solving a linear but ill-posed integral equation; step two turns that density into a conductivity image by solving a regularized nonlinear least-squares problem. For coupling constants in the measured range $10^{-7}$ to $10^{-9}\\,\\mathrm{Pa}^{-1}$ and noise up to $0.1\\%$, the main features of high- and low-contrast phantoms are recovered, with reconstruction quality controlled by the ratio of coupling strength to noise. A limited-angle variant reconstructs conductivity well near the measurement boundary. The authors note that exact knowledge of the internal acoustic pressure field is the main idealization.","feed_headline":"Simulation shows acousto-electric tomography can map conductivity","feed_subtitle":"Two-step inversion recovers phantom inclusions at realistic coupling and noise; quality tracks their ratio.","key_machinery":"The load-bearing identity is (2.3), $I_{i,j}(t)=-\\eta\\int_\\Omega p_j(x,t)H_i(x)\\,dx$, which turns boundary voltage differences into weighted integrals of the interior power density $H_i=\\sigma|\\nabla u_i|^2$ against known acoustic fields. Step 1 expands $H_i$ in Neumann eigenfunctions (Bessel functions on the disk) and solves the resulting ill-conditioned system $\\eta K\\hat H_i=I_i$ with a smoothness penalty. Step 2 minimizes $J(\\sigma)=\\sum_i\\|H_i(\\sigma)-z_i\\|_{L^1}+\\beta|\\sigma|_{TV}$ by iteratively reweighted quadratic subproblems. The ratio $\\eta/\\delta$ controls feasibility because the measured power signal is $O(\\eta)$ while electrical noise is independent of $\\eta$.","core_discovery":"The paper reports that a complete two-step inversion pipeline for acousto-electric tomography can reconstruct interior conductivity from boundary measurements under realistic parameter choices. On the authors' terms: with the perturbed conductivity model $\\sigma_p=\\sigma(1+\\eta p)$, the boundary power difference $I(t)$ is proportional to $\\int p H\\,dx$; collecting many acoustic source positions and boundary currents gives a linear system whose regularized solution yields the power density $H$. A second, total-variation-regularized optimization recovers $\\sigma$ from $H$. In simulated experiments with 27 acoustic fields, 3 boundary currents, and noise up to $0.1\\%$, the main features of high- and low-contrast phantoms are recovered for $\\eta$ from $10^{-7}$ to $10^{-9}\\,\\mathrm{Pa}^{-1}$; at the smallest $\\eta$ with $0.1\\%$ noise the inclusions are barely visible. Limited-angle measurements reconstruct conductivity well near the measurement boundary, matching earlier observations.","pith_inferences":["A natural stress test is to add realistic uncertainty to the acoustic field itself, such as transducer position, timing, or wave-speed errors; the paper's stated idealization suggests this will degrade the first step, but how quickly is an open quantitative question.","If $\\eta$ varies by tissue type, the $\\eta/\\delta$ control suggests reconstructions will be locally feasible wherever $\\eta/\\delta$ is large, producing spatially varying contrast-to-noise rather than global success or failure.","The two-step architecture could be used with other regularized linear solvers for step 1 and other data fidelities for step 2; the structural claim is the separation of the inversion into a linear ill-posed step and a nonlinear well-posed step."],"forward_implications":["For the high-contrast phantom, the main inclusions are recovered for $\\eta$ down to $10^{-8}\\,\\mathrm{Pa}^{-1}$ with up to $0.01\\%$ noise; at $0.1\\%$ noise the small square inclusion is nearly lost.","Lower noise can compensate for smaller coupling: reconstructions at $\\eta=10^{-8}$, $\\delta=0.1\\%$ and at $\\eta=10^{-9}$, $\\delta=0.01\\%$ look similar, matching the predicted $\\eta/\\delta$ scaling.","At zero noise, smaller $\\eta$ improves reconstruction quality because the first-order linearization behind (2.3) becomes more accurate.","With limited boundary access, inclusions close to the measurement boundary are recovered well, while deeper inclusions appear with reduced amplitude.","Step 1 requires regularization; the singular values of the discretized operator decay exponentially, so unregularized least squares is not a viable route."],"supporting_citations":[{"why":"Supplies the total-variation-regularized step-2 reconstruction algorithm the paper adapts and slightly smooths.","marker":"[1]"},{"why":"Provides the perturbed conductivity model $\\sigma_p = \\sigma(1+\\eta p)$ used throughout.","marker":"[3]"},{"why":"Foundational modelling of impedance tomography by elastic or acoustic deformation.","marker":"[4]"},{"why":"Introduces the Levenberg-Marquardt-style iteration for inverting the power density operator, used in step 2.","marker":"[7]"},{"why":"Earlier limited-angle acousto-electric tomography study whose near-boundary reconstruction observation the paper confirms.","marker":"[21]"},{"why":"Prior 2D and 3D AET reconstruction results that motivate the two-step quantitative approach.","marker":"[25]"},{"why":"Measured $\\eta \\approx 4.1\\times 10^{-8}\\,\\mathrm{Pa}^{-1}$ in rabbit heart, anchoring the realistic coupling range.","marker":"[26]"},{"why":"Measured $\\eta$ around $10^{-9}\\,\\mathrm{Pa}^{-1}$ in saline, anchoring the lower end of the range.","marker":"[33]"}],"fun_headline_variants":["AET inversion recovers conductivity from boundary data","Two-step inversion makes acousto-electric tomography feasible","Acousto-electric tomography: numerical feasibility demonstrated","Simulations show AET can map conductivity from boundary data","Limited-angle AET still resolves conductivity near boundary"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole pipeline assumes the acoustic pressure inside the body and the coupling constant $\\eta$ are known exactly; if either is uncertain, the boundary time series cannot be converted into power density.","fun_headline_variants_meta":{"raw":{"variants":["AET inversion recovers conductivity from boundary data","Two-step inversion makes acousto-electric tomography feasible","Acousto-electric tomography: numerical feasibility demonstrated","Simulations show AET can map conductivity from boundary data","Limited-angle AET still resolves conductivity near boundary"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000532,"raw_usage":{"total_tokens":2536,"prompt_tokens":894,"completion_tokens":1642,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":510,"completion_tokens_details":{"reasoning_tokens":1569}},"tokens_in":510,"tokens_out":1642,"duration_ms":11417,"temperature":1.0,"reasoning_tokens":1569,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:13:57.205121+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Use the same two-step algorithm on synthetic data where the pressure field used for inversion differs from the true field by a few percent in amplitude or timing, or where $\\eta$ varies spatially; if the main phantom inclusions disappear at error levels consistent with clinical ultrasound, the feasibility claim as stated would fail.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the total-variation-regularized step-2 reconstruction algorithm the paper adapts and slightly smooths."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the perturbed conductivity model $\\sigma_p = \\sigma(1+\\eta p)$ used throughout."},{"cited_title":"Ammari, E","cited_arxiv_id":null,"evidence_quote":"Foundational modelling of impedance tomography by elastic or acoustic deformation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the Levenberg-Marquardt-style iteration for inverting the power density operator, used in step 2."},{"cited_title":"Hubmer, K","cited_arxiv_id":null,"evidence_quote":"Earlier limited-angle acousto-electric tomography study whose near-boundary reconstruction observation the paper confirms."},{"cited_title":"Kuchment and L","cited_arxiv_id":null,"evidence_quote":"Prior 2D and 3D AET reconstruction results that motivate the two-step quantitative approach."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Measured $\\eta \\approx 4.1\\times 10^{-8}\\,\\mathrm{Pa}^{-1}$ in rabbit heart, anchoring the realistic coupling range."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Measured $\\eta$ around $10^{-9}\\,\\mathrm{Pa}^{-1}$ in saline, anchoring the lower end of the range."}],"review_version":1}