{"id":"694cf52f-2759-414b-9d20-5d489383864b","arxiv_id":"2505.07355","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"An integral-form imaging model cancels intra-pixel phase errors, permitting larger pixel sizes in computational-imaging ISAC environment sensing.","lead":"This paper proposes an integral-form computational imaging model for millimeter-wave ISAC that replaces point-sample pixel gains with surface integrals, aiming to allow larger imaging pixels without losing accuracy. The authors claim this extends computational imaging to large-scale wireless scenarios and support it with simulations.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Section IV's error analysis is not the error of the proposed model: it compares distances, but the model is a coherent integral of rapidly varying phases, so the claimed cancellation of large-pixel phase errors is not established.","rationale":"The reader's weakest_assumption focuses on the physical realism of the single-bounce, uniform-pixel model. That concern is legitimate, but I see a more direct, internal problem: the analytical error analysis in Section IV does not analyze the error of the model actually proposed. Even if the environment were exactly a set of uniformly scattering planar pixels, equations (9)-(14) measure error by distance differences, whereas the model in (2) is a coherent integral of complex exponentials. For large pixels, these two quantities diverge sharply because the phase oscillates many times across the pixel. This means the paper's theoretical support for the central claim is not merely incomplete but mismatched to its own forward model. The numerical results might still demonstrate the benefit of the integral model, but only if the simulator uses the same integral model as its ground truth or otherwise matches it; if that is the case, the comparison to the point-center baseline partly reflects model mismatch rather than a physically validated cancellation. If the simulator uses a different scattering model, the relationship to the analysis is unclear. The concern is concrete and testable, but it does not definitively falsify the approach; it shows that the claimed cancellation is not proven. I therefore keep the reader's CONDITIONAL verdict unchanged, with the condition that the authors supply a corrected error analysis or demonstrate explicitly that the simulation ground truth matches the integral model and that the coherent-integral amplitude remains sufficient at large pixel sizes.","tokens_in":8327,"tokens_out":5457,"duration_ms":58949,"concrete_test":"Compute, for a square pixel of side 1 m at 30 GHz with an antenna at broadside distance 10 m, the exact coherent integral I = ∫∫ λ/(4πd)e^{-2πjd/λ} dxdy over the pixel and the average-distance reference dp from Eq. (10). Compare arg(I) with 2πdp/λ and compare |I| with the point-model magnitude (λ/(4πd0) times pixel area). If arg(I) and 2πdp/λ differ by more than a few degrees, or if |I| is much smaller than the point-model magnitude, then Section IV's distance-based error metric is not the relevant error for the model in (2), and the claimed cancellation is unverified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the integral-form sensing matrix in (2) actually cancels the error caused by large pixel division for extended targets. The support for this claim is Section IV, but the error metrics there do not describe the model in (2). Equations (8)-(14) define phase errors as 2π|d - d_ref|/λ, where d_ref is either the pixel-center distance d0 or the average distance dp. The actual proposed forward model, however, is a coherent integral of λ/(4πd)e^{-2πjd/λ} over the pixel. The phase of this integral is not equal to the phase at the average distance dp when the integrand's phase varies significantly over the pixel; for a 1 m pixel at 30 GHz, the phase changes by hundreds of cycles across the pixel, so the integral can have a small magnitude and a phase determined by stationary-phase regions rather than by dp. Therefore, the statement in Section IV.B.2 that 'dp is close to dt and makes the error as small as possible' does not follow from the equations presented. The paper's own footnote 2 says amplitude effects are left to future work, but for large pixels the amplitude loss of the coherent integral is not a minor effect: it can be orders of magnitude below the point-model amplitude, which directly affects detection and CS reconstruction. Thus, even under the paper's single-bounce, uniform-pixel assumptions, the analytical cancellation claim is not established by the provided error analysis.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a computational imaging-based integrated sensing and communication (ISAC) method that aims to overcome the severe phase errors caused by large pixel division in millimeter-wave cellular scenarios. The key idea is to replace the conventional point-based propagation model (free-space gain evaluated at the pixel center, Eq. (1)) with an integral-form model that coherently integrates the scattered field over each pixel area (Eq. (2)). The environment sensing problem is reformulated as a compressed sensing recovery of the scattering coefficient vector, solved with the GAMP algorithm. The paper claims that the integral-form model cancels the large-pixel phase errors, and provides a performance analysis in Section IV plus numerical simulations in Section V, comparing against the baseline center-point model in terms of missed detection and false alarm rates.","tokens_in":1478,"tokens_out":1478,"duration_ms":42704,"significance":"If the central claim is correct, the approach would be a meaningful step toward extending computational imaging to large-scale wireless sensing, potentially allowing pixel sizes much larger than the wavelength and thereby reducing the number of unknowns and computational cost. The core idea is appealing and the simulation results are suggestive. However, the paper's analytical support is not aligned with its actual model: the error analysis in Section IV is based on distance differences (phase arguments) and average distances, while the proposed forward model in Eq. (2) is a coherent integral of rapidly varying complex exponentials. The phase and amplitude behavior of that integral is not captured by the provided metrics. Since the cancellation claim is the central contribution, the current manuscript leaves this point unestablished. If the analysis were redone for the true integral model, and if the simulation methodology were clarified, the paper would likely be a valuable contribution to computational imaging for ISAC.","major_comments":[{"comment":"The error analysis for the proposed model does not describe the model in Eq. (2). Equations (13) and (14) define the phase error in terms of the difference between the actual distance d_t and the average distance d_p, i.e., 2π|d_t - d_p|/λ. But the proposed forward model coherently integrates λ/(4π d) e^(-j2π d/λ) over the pixel; the phase of this integral is not equal to the phase at the average distance when the phase varies by many cycles across the pixel. For a 1 m pixel at 30 GHz, the phase changes by hundreds of cycles, and the integral magnitude can be orders of magnitude smaller than the center-point value. Therefore the claim in Section IV.B.2 that d_p is close to d_t and makes the error as small as possible does not establish cancellation of the phase error of the actual model. The analysis needs to be reworked in terms of the complex integral, or the paper should explicitly label the distance-based analysis as a heuristic that is not a bound on the true model error.","section":"Section IV.B, Eqs. (11)-(14)"},{"comment":"The paper states that errors resulting from pixel area exceeding the target area or uneven scattering primarily affect amplitude and will be left to future work. For large pixels (e.g., 1 m at 30 GHz, i.e., 100 wavelengths), the amplitude of the coherent integral in Eq. (2) can be much smaller than the point-model amplitude due to phase cancellation across the pixel. Such amplitude loss is not a minor effect: it directly degrades detection and compressed sensing reconstruction. The paper should either incorporate amplitude effects into the analysis or provide a quantitative argument that they are negligible in the scenarios considered.","section":"Section III.A, footnote 2 and accompanying text"},{"comment":"The simulation methodology is not fully specified. The text says ray tracing from [16] generates the received signals, but it is unclear whether the ground-truth targets are point scatterers or extended surfaces. If the targets are point-like, then the proposed integral model in Eq. (2) integrates over pixels that contain only a sparse point, which is not the same as the planar-target analysis in Section IV.B; this would misrepresent the source of the improvement. The authors should clarify the target geometry used in the simulations, specify how the sensing matrix A is constructed (integration rules, pixel sizes, etc.), and ideally include a case with an extended surface target to validate the claimed cancellation under exactly the conditions analyzed.","section":"Section V.A, simulation setup"}],"minor_comments":[{"comment":"The author list contains \"ning ming\" with a space, which appears to be a placeholder or an error; please check the author names.","section":"Author list"},{"comment":"The phrase \"It is worthy noted\" should be \"It is worth noting\".","section":"Section II.A, footnote 1"},{"comment":"The update for sigma_x_ns(i+1) uses sigma_r_ns(i), which is not defined; this is likely a typo for sigma_u_ns(i).","section":"Algorithm 1, line 6"},{"comment":"The constraint is written as ||H_k - ...|| but the vectorized notation introduced in Eq. (5) suggests the constraint should be on the stacked vector; please check the indexing consistency.","section":"Eq. (6)"},{"comment":"The horizontal axis label \"Scatterer proportion\" should be defined in the caption as (l_t w_t)/(l_s w_s) to match the text in Section IV.B.","section":"Figure 5"}],"recommendation":"major_revision","confidential_remarks":"The paper is from a well-known group in ISAC, and the simulation results are promising. However, the analytical section is not aligned with the actual model, and the central claim of error cancellation is not established as written. The authors should be encouraged to redo the error analysis for the coherent integral model or to clearly state the heuristic nature of the distance-based analysis. The simulation setup also needs to be more transparent. I recommend major revision rather than rejection, because the underlying idea has merit and the issues are fixable within the paper's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Good that you asked. The one thing to know: the paper's core modeling move—replace the point-center propagation gain with a coherent integral over the pixel—is sensible and probably useful for large-pixel ISAC, but the paper's own Section IV error analysis does not actually establish the cancellation claim that the abstract promises. The stress-test note is right: equations (8)-(14) define phase error as average absolute distance difference, while the actual model in (2) is a coherent integral of rapidly varying phases. For a 1 m pixel at 30 GHz the phase changes by hundreds of cycles, so the integral's magnitude and phase are not governed by the average distance dp. Section IV.B.2's statement that dp is close to dt and hence minimizes error is therefore unsupported. Footnote 2 explicitly defers amplitude effects, but the amplitude loss of the coherent integral is not a minor effect—it can be orders of magnitude below the point-model amplitude, which directly affects detection.\n\nWhat's genuinely new: the integral-form pixel model in (2) is a natural refinement of the point-center gains in [11],[12], but the numerical demonstration that large pixels (up to 1 m at 30 GHz) can still yield usable MD/FA rates is new to this paper. That is a real practical gain for mmWave environment sensing. The CS formulation and GAMP reconstruction are standard but appropriate. I give credit for not fitting parameters to force the result; the model is an independent reformulation.\n\nThe soft spots beyond the error-analysis mismatch: the 'first time' claim is overstated—[11] and [12] already do computational imaging in wireless scenarios; the novelty is the integral treatment, not the application. The numerical validation is thin: one cross-target scenario, no statistical variation, no code, arbitrary detection threshold of 0.5, and no comparison with other large-pixel approaches. Also the single-bounce, uniform-pixel assumption is taken as premise; that's fine for a first paper but should be flagged more prominently.\n\nOverall: the idea is worth engaging. A serious referee should see it, but the paper needs a major revision—either replace Section IV with a proper analysis of the coherent integral (or at least a numerical phase-error study of the actual model), and strengthen the simulations. If I were handling it, I'd accept for review and send back for heavy revision.","headline":"The integral-form pixel model is a sensible and likely useful refinement for large-pixel ISAC, but the paper's own error analysis does not actually support the cancellation claim; the numerical results are suggestive, not conclusive.","tokens_in":9148,"tokens_out":2110,"would_cite":false,"duration_ms":19586,"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":"Replacing center-point propagation with a pixel-area integral lets millimeter-wave computational imaging use large pixels without the usual phase-error blowup, extending the method to large-scale sensing.","keywords":["integrated sensing and communication","computational imaging","pixel division","phase error cancellation","compressed sensing","millimeter-wave sensing","generalized approximate message passing","large-scale environment sensing"],"falsifier":"Run the proposed estimator on ray-traced or measured data from a scene with a strong second-bounce reflection off a large planar surface, or with a target whose reflectivity varies across a pixel; if reconstruction miss-detection and false-alarm rates rise well above the single-bounce uniform-pixel simulation, the integral-form cancellation is incomplete for that propagation regime.","tokens_in":8154,"feed_emoji":"📡","tokens_out":2529,"duration_ms":27554,"temperature":0.7,"pith_summary":"Computational imaging in ISAC systems conventionally divides the environment into pixels and models each pixel's propagation by a single center-point distance. When pixels grow beyond a wavelength, that center-point approximation produces near-random phase errors and sensing fails. The paper proposes an integral-form model that averages the free-space Green's function over each pixel, which the authors show cancels the dominant phase error for extended objects. This makes it feasible to sense large-scale millimeter-wave environments with far fewer, larger pixels, reducing computational and antenna overhead. The claimed contribution is a first step toward applying computational imaging outside confined small-scale regions.","feed_headline":"Pixel-area integral removes big-pixel sensing error in mmWave ISAC","feed_subtitle":"Center-point propagation fails for large pixels; integrating over each pixel's whole area preserves accuracy in large-scale environments.","key_machinery":"The central object is the pixel-integrated propagation gain, defined in equation (2) as $\\tilde{H}^{\\mathrm{Tx}}_k(n_s,n_T) = \\int_{x_0-l_s/2}^{x_0+l_s/2}\\int_{y_0-w_s/2}^{y_0+w_s/2} \\frac{\\lambda_k}{4\\pi d l_s w_s} e^{-2j\\pi d/\\lambda_k} \\, dx\\,dy$ with $d=\\sqrt{(x_T-x)^2+(y_T-y)^2}$. This integral replaces the conventional center-point gain of equation (1), and it carries the argument by averaging the phase of the spherical wave over the entire pixel footprint, so that a target anywhere in the pixel is represented by a phase close to its own. The compressed sensing reconstruction, solved by the GAMP algorithm, then estimates the scattering coefficients from the jointly processed multi-carrier, multi-antenna measurements.","core_discovery":"The paper argues that the severe sensing errors caused by large pixel division in traditional computational imaging are not inherent but arise from modeling each pixel as a point at its center. Replacing the discrete center-point propagation factor with a two-dimensional integral of the propagation phase over the pixel area removes the phase error that otherwise becomes effectively random when pixel size exceeds one wavelength. For planar targets that fill a pixel, the integral-form average distance converges to the true target distance, so the error drops sharply as the scatterer proportion within a pixel grows. The received signal model is then cast as a compressed sensing problem and solved with a Bernoulli-Gaussian sparse prior, yielding accurate environmental images even with pixel sizes of one meter at 30 GHz, where the baseline center-point method fails.","pith_inferences":["The same integral-form cancellation should extend to 3D volumetric pixels, suggesting a direct route to large-scale volumetric ISAC imaging with manageable pixel counts.","Because the paper shows the advantage is specifically for extended surface targets and not point targets, the practical gain is best stated for planar or large scatterers; point-like targets still require fine pixels.","A natural testable extension is to use nonuniform or boundary-adaptive pixel meshes that align with object edges, which could push the residual edge error further down.","The model implicitly assumes single-bounce scattering; if multi-bounce or occlusion is significant, the integral-form averaging alone will not recover the sensing accuracy shown in the single-bounce simulations."],"forward_implications":["Pixel sizes can be many wavelengths without the phase-error collapse that plagues center-point computational imaging, enabling a drastic reduction in the number of pixels and the associated sensing overhead.","Computational imaging becomes practical for large-scale millimeter-wave wireless environments, such as outdoor cellular scenes, where fine pixel grids would be computationally prohibitive.","The residual phase error for planar targets is governed by the fraction of a pixel that the target fills, so errors concentrate at object edges rather than throughout the image.","The method naturally inherits the compressed sensing framework, so sparsity-promoting reconstruction algorithms and their convergence guarantees apply unchanged.","The integral computation per pixel can be precomputed and parallelized, so the added modeling cost does not scale with reconstruction complexity."],"supporting_citations":[{"why":"Provides the baseline computational imaging ISAC system whose center-point propagation model the paper replaces.","marker":"[11]"},{"why":"Establishes the multi-view computational imaging approach that the proposed integral model extends to large-scale scenarios.","marker":"[12]"},{"why":"Supplies the compressed sensing theory underlying the sparse reconstruction formulation.","marker":"[13]"},{"why":"Provides the OFDM channel estimation procedure that isolates the multipath propagation gain used as sensing data.","marker":"[14]"},{"why":"Defines the GAMP algorithm used to solve the compressed sensing reconstruction problem.","marker":"[15]"},{"why":"Provides the ray tracing method used to generate received signals and propagation gains in the numerical validations.","marker":"[16]"}],"fun_headline_variants":["Pixel-area integral fixes large-pixel ISAC sensing errors","Integral over pixel area beats point-model in mmWave ISAC","Large-pixel ISAC error canceled by integral imaging model","Computational imaging gets integral fix for large pixels","ISAC with big pixels: integrate over area, not point"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The environment is modeled as a set of independent, uniformly scattering pixels whose received field is the single-bounce coherent sum of free-space waves integrated over each pixel; if significant multi-bounce, occlusion, or per-pixel reflectivity variation occurs, the claimed error cancellation does not carry over.","fun_headline_variants_meta":{"raw":{"variants":["Pixel-area integral fixes large-pixel ISAC sensing errors","Integral over pixel area beats point-model in mmWave ISAC","Large-pixel ISAC error canceled by integral imaging model","Computational imaging gets integral fix for large pixels","ISAC with big pixels: integrate over area, not point"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000139,"raw_usage":{"total_tokens":1108,"prompt_tokens":848,"completion_tokens":260,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":464,"completion_tokens_details":{"reasoning_tokens":178}},"tokens_in":464,"tokens_out":260,"duration_ms":2664,"temperature":1.0,"reasoning_tokens":178,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T22:18:53.857663+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the proposed estimator on ray-traced or measured data from a scene with a strong second-bounce reflection off a large planar surface, or with a target whose reflectivity varies across a pixel; if reconstruction miss-detection and false-alarm rates rise well above the single-bounce uniform-pixel simulation, the integral-form cancellation is incomplete for that propagation regime.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the baseline computational imaging ISAC system whose center-point propagation model the paper replaces."},{"cited_title":"Environment sensing considering the occlusion effect: A multi-view approach,","cited_arxiv_id":null,"evidence_quote":"Establishes the multi-view computational imaging approach that the proposed integral model extends to large-scale scenarios."},{"cited_title":"Compressed sensing,","cited_arxiv_id":null,"evidence_quote":"Supplies the compressed sensing theory underlying the sparse reconstruction formulation."},{"cited_title":"On channel estimation in OFDM systems,","cited_arxiv_id":null,"evidence_quote":"Provides the OFDM channel estimation procedure that isolates the multipath propagation gain used as sensing data."},{"cited_title":"Generalized approximate message passing for estimation with random linear mixing,","cited_arxiv_id":null,"evidence_quote":"Defines the GAMP algorithm used to solve the compressed sensing reconstruction problem."},{"cited_title":"Physics-inspired target shape detection and reconstruc- tion in mmWave communication systems,","cited_arxiv_id":null,"evidence_quote":"Provides the ray tracing method used to generate received signals and propagation gains in the numerical validations."}],"review_version":1}