{"id":"0f600418-8ccc-4ff8-802e-d4ecf13ce1d8","arxiv_id":"1908.01903","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Simulated sparse sampling shows that compressed sensing can reconstruct QPI maps from as few as 2 to 5 percent of STM measurement points.","lead":"This paper shows in simulations that compressed sensing can recover quasiparticle interference patterns in scanning tunneling microscopy from as little as 2 to 5 percent of the usual measurements. It also uses a traveling-salesman route to cut wasted STM tip motion, potentially making slow QPI mapping much faster.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's sparsity premise is overstated: the simulated Cu(111) QPI pattern is a continuous ring in Fourier space, not 'few nonzero coefficients,' so the 5% recovery claim may not be a genuine compressed-sensing advantage.","rationale":"The reader identified the real-data sparsity assumption as the load-bearing weakness; this stress-test sharpens that concern by showing that the paper's own idealized simulation already violates the literal 'few nonzero coefficients' premise. The QPI of a two-dimensional surface state with point scatterers is concentrated on a circle in reciprocal space, not on a small set of isolated pixels, so the number of significant coefficients grows with the grid size rather than remaining constant. This does not necessarily invalidate the method—compressed sensing can sometimes recover structured sparse or low-complexity signals beyond strict s-sparsity—but the paper does not provide the required analysis or evidence for that broader guarantee. The lack of error bars, single realizations, and any test on experimental or higher-complexity simulated data reinforces the conditional nature of the claim. The reader's CONDITIONAL verdict remains appropriate; the concern is real but addressable with additional statistical and real-data validation.","tokens_in":5739,"tokens_out":2316,"duration_ms":27739,"concrete_test":"Reconstruct the Figure 2 simulation at N = 1024 x 1024 and threshold the Fourier QPI pattern at a noise floor (e.g., 1% of the maximum coefficient) to count the number s of significant coefficients. Then run at least 20 independent compressed-sensing trials at p = 0.02, 0.05, and 0.18 with different random masks, recording normalized l2 error and support overlap. If s is substantially larger than pN/log N, or if recovery quality varies strongly across masks, the 'reliable recovery' claim fails even for the paper's own idealized data. Additionally, repeat with a broadened QPI ring (multiple scattering vectors or finite band lifetime) to test whether the sparse model holds outside the single, sharp-ring example.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim relies on the abstract's assertion that 'CS relies on sparsity in a vector domain, here given by few nonzero coefficients in Fourier space.' But the simulated QPI patterns shown in Figures 1b and 2c-d are rings at q = 2k with finite width, not a small set of isolated nonzero pixels. On a 1024 x 1024 grid, such a ring occupies on the order of hundreds to thousands of Fourier coefficients, which is not 'few' in the sense required by s-sparse compressed sensing guarantees. The reported recovery at 5% random sampling therefore may simply reflect that 50,000 random measurements can estimate a ring-like support with a few thousand coefficients, not a fundamental reduction from Nyquist sampling. The paper also does not report quantitative error bars, single-realization results, or the actual sparsity s of the recovered patterns, so the relationship between sampling fraction pN and information content s log N is never established. If the QPI pattern is only mildly sparse, the method's 'reliable recovery' from 2-5% sampling is not demonstrated, and the speed-up claim loses its theoretical grounding even for the idealized simulation.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a compressed-sensing (CS) approach to accelerate quasiparticle interference (QPI) mapping by scanning tunneling microscopy (STM). Instead of measuring the local density of states (LDOS) on a full grid, the authors randomly sample a small fraction p of points, reconstruct the QPI pattern in Fourier space by l1 minimization (SPGL1 basis pursuit denoising), and inverse Fourier transform to obtain LDOS. They simulate a Cu(111) surface state with point scatterers and white noise, demonstrating reconstruction with 20% sampling on a 64x64 grid and 5% random sampling on a 1024x1024 grid. They also introduce 'informed sampling,' with denser sampling near known scatterers, claimed to work at 2%, and combine the sampling points with a traveling-salesman route to reduce tip travel time. The central claim is that QPI information can be reliably recovered from a small fraction of usual measurements, enabling faster QPI experiments.","tokens_in":5967,"tokens_out":5380,"duration_ms":53338,"significance":"If validated, the method would directly address a recognized bottleneck in STM: the serial, time-consuming acquisition of QPI maps. The paper demonstrates a qualitatively correct recovery of a known simulated QPI pattern at 5% random sampling with a standard solver, and the random-sampling portion is largely parameter-free. The informed-sampling idea is physically motivated and the TSP routing is practical. However, the evidence is limited to idealized simulations with single realizations, no statistical error bars, and a post-hoc tuning of the informed-sampling kernel. The significance is therefore potential rather than demonstrated; the paper is a promising proof-of-concept that currently overstates the reliability and generality of the method.","major_comments":[{"comment":"The sparsity premise underlying the CS claim is not established. The abstract states that QPI is sparse because it has 'few nonzero coefficients in Fourier space,' but the QPI patterns shown are continuous rings at q=2k_F with finite width plus Bragg peaks; on a 1024x1024 grid these features contain hundreds to thousands of significant coefficients, not 'few.' The paper never reports the sparsity s of the recovered QPI, nor the ratio of the number of measurements pN to s log N, which is the quantity that governs CS performance. Consequently, the 5% random-sampling recovery may simply reflect the estimation of a low-dimensional ring support from 50,000 samples, rather than a genuine compressed-sensing advantage. Please quantify the effective sparsity (e.g., number of coefficients above a threshold) and discuss the results in relation to CS sampling bounds.","section":"Abstract; Figs. 1b, 2c–d"},{"comment":"The informed-sampling result at 2% sampling is circular because the HWHM of the Lorentzian sampling distribution is selected as the 'optimal' value on the same simulated data used to demonstrate recovery. A parameter tuned to maximize recovery on the test example cannot support a general claim that informed sampling 'achieves QPI recovery even at 2% subsampling.' Please validate HWHM selection by an independent criterion (e.g., a physical decay length or cross-validation on training data) and report performance over multiple random masks under a fixed, pre-specified HWHM.","section":"Fig. 2e; text on informed sampling"},{"comment":"All reported recovery results appear to be single realizations of the random sampling mask and noise. The word 'reliably' in the abstract is not backed by any statistical measure: no recovery rate over repeated masks, no error bars, and no threshold defining a successful reconstruction. In addition, the SPGL1 noise-tolerance parameter sigma is an adjustable free parameter, but its values and sensitivity are not reported. Please add a statistical analysis over at least tens of random masks/noise realizations, a success criterion, and a description of how sigma was set.","section":"Methods; Fig. 2c–f"},{"comment":"The abstract and conclusion make broad claims ('reliably recover the QPI information from a fraction of the usual local density of state measurements'; 'transformative for the exploration of 2D quantum materials') based on an idealized simulation with a few point scatterers and white noise. Real QPI maps contain multiple overlapping scattering vectors, broadened features, non-white noise, and experimental artifacts. The limitations are only implicit in the Methods. Please either add a dedicated limitations paragraph and temper the abstract, or include a more realistic test case (e.g., multiple scattering sites with varying strengths, finite lifetime broadening) to support the general claim.","section":"Abstract; Conclusion"}],"minor_comments":[{"comment":"'Data-recording is serial' should be 'Data recording is serial,' and the semicolon after 'slow technique' should be a period.","section":"Abstract"},{"comment":"'with spar sity and number o f recovered coefficients indicated' contains spacing typos; correct to 'with sparsity and number of recovered coefficients indicated.'","section":"Fig. 2 caption"},{"comment":"'a TSP or sparse line-hopping could provide provide a fast overview' has a duplicated word 'provide.'","section":"Methods"},{"comment":"'complimentary noise rejection' should be 'complementary noise rejection.'","section":"Text near Fig. 1"},{"comment":"'using a traveling salesman between the distributed measurement locations' is unclear; suggest 'using a traveling-salesman path connecting the measurement locations.'","section":"Fig. 1 caption"},{"comment":"The text refers to 'green circles' marking the informed-sampling regions, while the figure caption describes them as 'rings'; please reconcile the terminology.","section":"Fig. 2 and main text"}],"recommendation":"major_revision","confidential_remarks":"The paper would benefit from a broader literature review: the authors cite the sparse-sampling STEM work (Ref. 30) but do not discuss prior compressed-sensing applications to STM in other contexts, which may affect the novelty framing. Providing the simulation code and data would also strengthen reproducibility. These points are for the editor."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [Colleague],\n\nThis is a genuine new application of compressed sensing to QPI-STM, and the 5% random-sampling recovery on a simulated 1024x1024 surface is a real result. It is not the game-changer the abstract claims, but the core idea is sound and worth engaging.\n\nThe stress-test worry about 'few nonzero coefficients' is partly right. The simulated QPI pattern is a ring plus six Bragg spots, not a handful of pixels. On a 1024x1024 grid that ring occupies hundreds to thousands of coefficients, so the paper overstates the sparsity. But a ring is still low-dimensional; recovering it from 5% of the measurements is consistent with compressed sensing of a compressible object, not necessarily exact s-sparse recovery. The paper never reports the actual sparsity level s or the number of recovered coefficients versus pN, so the theoretical grounding is incomplete. That is a gap worth fixing, not a fatal flaw.\n\nWhat is genuinely new: applying CS to QPI-STM, the informed-sampling variant that concentrates measurements around scatterers, and the TSP tip-routing to shorten travel. The informed-sampling 2% result is weaker than it looks because the Lorentzian HWHM was chosen to be optimal on this same simulated example (Fig. 2e). That is post-hoc tuning, and the authors should say so. The random-sampling 5% result is parameter-free and tested against a known ground truth, so the central CS claim is not circular.\n\nThe paper has no error bars, no multiple realizations, no noise-level sweeps, and no real STM data. The single-realization figures make the recovery look cleaner than a typical result would. The 291-hour comparison is fair for the assumed 1 s per spectrum, but the 'transformative' language in the abstract is too strong.\n\nCitation pattern is fine: the key CS and QPI-STM references are there, and the prior sparse-STEM work is cited. No code or data is shipped, which is a missed opportunity for a simulation study.\n\nWho is this for: experimental STM groups thinking about faster QPI mapping, and CS practitioners who want a concrete scattering problem. I would send it to peer review. With added error statistics, an honest treatment of the tuned HWHM, and a test on a more realistic spectral function, the paper would be solid. As is, it deserves a careful referee, not a desk rejection.","headline":"A plausible and potentially useful CS-for-QPI methods paper; the 5% random-sampling result is real, but the sparse-ring framing and the tuned informed-sampling HWHM need work.","tokens_in":6523,"tokens_out":3837,"would_cite":false,"duration_ms":75148,"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":"This paper claims that compressed sensing can recover quasiparticle interference maps from as little as 2–5% of the local density of state measurements, a speed-up that would make systematic STM band-structure studies practical.","keywords":["compressed sensing","quasiparticle interference","scanning tunneling microscopy","sparse sampling","Fourier transform","local density of states","traveling salesman problem","Cu(111)"],"falsifier":"Take an experimental STM QPI dataset on a known surface, reconstruct from randomly chosen 5% and 2% subsets with basis pursuit denoising, and compare the recovered scattering vectors and intensities to the full map; if the peaks shift, merge, or spurious peaks appear under realistic non-white noise and overlapping scattering vectors, the claimed sampling fractions do not transfer to experiment.","tokens_in":5502,"feed_emoji":"🔬","tokens_out":5833,"duration_ms":59297,"temperature":0.7,"pith_summary":"The paper argues that quasiparticle interference mapping with a scanning tunneling microscope, normally a serial and time-consuming measurement, can be replaced by compressed sensing. Because a QPI pattern is sparse in Fourier space, randomly sampling a small fraction of the local density of states and solving a basis-pursuit reconstruction problem yields the same band-structure information. The authors demonstrate this on simulated Cu(111) surfaces, recovering a 1024×1024 QPI pattern from 5% random sampling and from 2% informed sampling concentrated near scatterers. They also route the STM tip between measurement points as an open traveling-salesman problem to cut travel time. If the sparsity assumption transfers to real materials, the method would shrink QPI experiments from day-long runs to a few hours.","feed_headline":"Quasiparticle maps recovered from 5% of STM data","feed_subtitle":"Compressed sensing exploits sparse Fourier patterns to cut scanning tunneling microscopy time by an order of magnitude.","key_machinery":"The load-bearing mechanism is compressed sensing via basis pursuit denoising. The QPI pattern is modeled as sparse in Fourier space, the measurement matrix connects that pattern to the sparsely sampled LDOS values, and recovery minimizes ∥x∥₁ subject to a noise-adjusted consistency constraint. Two further elements carry the practical speed-up: a random sampling mask, optionally informed by known scatterer locations or designed to exclude problematic regions, and an open traveling-salesman routing of the STM tip solved with a genetic algorithm, because tip travel time is a real cost in the measurement.","core_discovery":"The central claim is that a QPI pattern contains only a few significant Fourier coefficients, exactly the condition compressed sensing requires. The paper treats each grid point as a measurement, builds a random sampling mask, collects a fraction of the LDOS values, and reconstructs the full QPI pattern by minimizing the ℓ1 norm of the Fourier coefficients subject to consistency with the measured values. On simulated Cu(111) data with Gaussian noise, random sampling at 5% recovers the QPI map, and informed sampling—denser near known scatterers—recovers it at 2%. The recovered pattern matches the fully sampled map in its surface-state wavevector and Bragg peaks, and an inverse Fourier transform reproduces the original LDOS modulations while suppressing noise.","pith_inferences":["If experimental QPI patterns are less sparse than the simulated Cu(111) case—broad bands, overlapping scattering vectors, non-white noise—the required sampling fraction will rise; the lasting claim is the general framework, not a universal 2% guarantee.","The same sparsity-and-compressed-sensing logic should apply to other spatially resolved spectroscopies that image periodic modulations, such as standing-wave maps in superconductors or spin-textured surfaces, wherever the Fourier pattern is sparse.","Because sampling masks and traveling-salesman paths can be precomputed, one could assemble a library of optimized masks and use the time correlation introduced by the tip path to correct drift during long sparse acquisitions.","A direct test of the paper's weakest point would be a blinded comparison on real experimental data, reconstructing from subsets and checking whether recovered scattering vectors and intensities match the fully sampled map."],"forward_implications":["A 1024×1024 QPI map is recovered from 5% randomly chosen LDOS points, implying roughly an order-of-magnitude reduction in measurement time for a typical QPI experiment.","Informed sampling around known impurities lowers the required fraction to 2%, making the method usable on samples with few scatterers or tight time limits.","The same informed-sampling mask can exclude step edges or unstable impurities before measuring, avoiding wasted data acquisition.","Near-optimal traveling-salesman tip routing cuts tip travel distance by about 63% relative to a full raster, adding further time savings.","The approach requires no hardware changes, so existing STM systems could adopt it as a software-level measurement and reconstruction protocol."],"supporting_citations":[{"why":"Supplies compressed sensing theory: sparsity allows recovery from far fewer measurements than Nyquist sampling requires.","marker":"[13]"},{"why":"Establishes stable signal recovery from incomplete and inaccurate measurements, the theoretical basis for basis pursuit denoising used here.","marker":"[14]"},{"why":"Defines Fourier-transform STM, the method that turns LDOS modulations into momentum-space QPI patterns.","marker":"[3]"},{"why":"Demonstrates quasiparticle interference imaging in a high-temperature superconductor, the experimental target this paper aims to speed up.","marker":"[4]"},{"why":"Provides the sparse-reconstruction solver used to perform the ℓ1-minimization recovery.","marker":"[28]"},{"why":"Supplies the algorithmic basis for the solver's basis-pursuit denoising step.","marker":"[29]"},{"why":"Provides the genetic-algorithm solution to the open traveling-salesman problem used to route the STM tip efficiently.","marker":"[15]"}],"fun_headline_variants":["Sparse sampling recovers QPI maps from 5% of STM data","Compressed sensing enables QPI mapping from 2% of measurements","Fast STM QPI mapping via sparse Fourier sampling","QPI maps from under 5% of STM measurements"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument stands on the premise that real QPI patterns are sparse enough in Fourier space that 2–5% of randomly chosen measurement points still contain the full scattering information.","fun_headline_variants_meta":{"raw":{"variants":["Sparse sampling recovers QPI maps from 5% of STM data","Compressed sensing enables QPI mapping from 2% of measurements","Fast STM QPI mapping via sparse Fourier sampling","QPI maps from under 5% of STM measurements"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000763,"raw_usage":{"total_tokens":3343,"prompt_tokens":860,"completion_tokens":2483,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":476,"completion_tokens_details":{"reasoning_tokens":2409}},"tokens_in":476,"tokens_out":2483,"duration_ms":18427,"temperature":1.0,"reasoning_tokens":2409,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:00:05.438414+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take an experimental STM QPI dataset on a known surface, reconstruct from randomly chosen 5% and 2% subsets with basis pursuit denoising, and compare the recovered scattering vectors and intensities to the full map; if the peaks shift, merge, or spurious peaks appear under realistic non-white noise and overlapping scattering vectors, the claimed sampling fractions do not transfer to experiment.","supporting_citations":[{"cited_title":"J., Romberg, J","cited_arxiv_id":null,"evidence_quote":"Establishes stable signal recovery from incomplete and inaccurate measurements, the theoretical basis for basis pursuit denoising used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines Fourier-transform STM, the method that turns LDOS modulations into momentum-space QPI patterns."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Demonstrates quasiparticle interference imaging in a high-temperature superconductor, the experimental target this paper aims to speed up."},{"cited_title":"van den & Friedlander, M","cited_arxiv_id":null,"evidence_quote":"Provides the sparse-reconstruction solver used to perform the ℓ1-minimization recovery."},{"cited_title":"van den & Friedlander, M","cited_arxiv_id":null,"evidence_quote":"Supplies the algorithmic basis for the solver's basis-pursuit denoising step."},{"cited_title":"Open Traveling Salesman Problem - Genetic Algorithm","cited_arxiv_id":null,"evidence_quote":"Provides the genetic-algorithm solution to the open traveling-salesman problem used to route the STM tip efficiently."}],"review_version":1}