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REVIEW 4 major objections 6 minor 30 references

Sparse Sampling for Fast Quasiparticle Interference Mapping

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 1908.01903 v1 pith:F3LLJCDX submitted 2019-08-05 cond-mat.other physics.data-an

Jens Oppliger , Fabian Donat Natterer This is my paper · ORCID
classification cond-mat.otherphysics.data-an
keywords compressedsensingquasiparticleinterferencescanningtunnelingmicroscopysparsesamplingFouriertransformlocaldensityofstatestravelingsalesmanproblemCu(111)
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

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.

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 (4)
  1. [Abstract; Figs. 1b, 2c–d] 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.
  2. [Fig. 2e; text on informed sampling] 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.
  3. [Methods; Fig. 2c–f] 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.
  4. [Abstract; Conclusion] 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.
minor comments (6)
  1. [Abstract] 'Data-recording is serial' should be 'Data recording is serial,' and the semicolon after 'slow technique' should be a period.
  2. [Fig. 2 caption] 'with spar sity and number o f recovered coefficients indicated' contains spacing typos; correct to 'with sparsity and number of recovered coefficients indicated.'
  3. [Methods] 'a TSP or sparse line-hopping could provide provide a fast overview' has a duplicated word 'provide.'
  4. [Text near Fig. 1] 'complimentary noise rejection' should be 'complementary noise rejection.'
  5. [Fig. 1 caption] 'using a traveling salesman between the distributed measurement locations' is unclear; suggest 'using a traveling-salesman path connecting the measurement locations.'
  6. [Fig. 2 and main text] The text refers to 'green circles' marking the informed-sampling regions, while the figure caption describes them as 'rings'; please reconcile the terminology.

Circularity Check

1 steps flagged · score 5.0 of 10

Informed-sampling 2% result depends on a fitted HWHM; random-sampling 5% recovery is an independent demonstration.

  1. fitted input called prediction [Figure 2e caption and Section "Informed Sampling" discussion]
    "The comparison with random-point-sampling in Figure 2c,d shows that IS achieves QPI recovery even at 2% subsampling when random-point-sampling has already failed. ... e, optimal radius (HWHM) for a Lorentzian probability distribution used in the informed sampling method."

    The informed-sampling mask is built from a Lorentzian probability distribution whose HWHM is reported as "optimal." The 2% recovery result is demonstrated using this optimized radius. Because the radius was selected on the same simulated dataset to produce the best recovery, the claim that informed sampling achieves recovery at 2% is a fitted demonstration, not an independent prediction. The recovery success at 2% is effectively the target used to choose the parameter, so that particular result is partly forced by construction. The random-point-sampling result at 5% is parameter-free and remains an independent demonstration, but the stronger informed-sampling claim depends on the fitted HWHM.

full rationale

The central compressed-sensing pipeline is not circular: the authors simulate a known Cu(111) LDOS, subsample it randomly, and recover the QPI pattern with a standard l1-minimization solver (SPGL1) against a known ground truth. The 5% random-point-sampling demonstration is parameter-free and externally checkable, so it provides genuine support for the method. However, the informed-sampling variant, which yields the stronger 2% claim, uses a sampling mask whose Lorentzian HWHM is explicitly called "optimal" in the figure caption. The paper does not describe a held-out validation or a first-principles rule for setting this radius, so the 2% recovery is a fitted demonstration rather than a prediction. The abstract's sparsity assertion is a premise about real QPI data and is better evaluated as a validity or correctness concern than as circular reasoning; it is not derived from the target claim. There are no load-bearing self-citations in the paper. The score reflects one fitted-input step in part of the central claim, while the random-sampling result remains independent.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim depends on several domain assumptions that are plausible but untested against real data. The most significant free parameters are the sampling fraction and the informed-sampling HWHM, the latter being fitted to the simulated example. No invented physical entities are introduced.

free parameters (5)
  • sampling fraction p = 20% (Fig 1), 2-18% (Fig 2), 8% (Fig 3)
    User-chosen subsampling level that determines the speedup; the claimed recovery thresholds (5% random, 2% informed) depend on p.
  • noise tolerance sigma in SPGL1 BPDN = not specified
    Adjustable threshold in the basis pursuit denoising objective ||Ax - b||_2 <= sigma; the paper does not state how sigma is set, which affects recovery quality.
  • Gaussian noise amplitude = 0.2 of LDOS standard deviation
    Added to the simulated LDOS in Figure 1; chosen arbitrarily, and all recovery results are shown for this single noise level.
  • number of scattering sites = 1 (Fig 1), 10 (Fig 2), unspecified for Fig 3
    Determines the sparsity and structure of the simulated QPI pattern; no analysis of sensitivity to this choice.
  • HWHM of Lorentzian sampling distribution (informed sampling) = optimal value fitted per Fig 2e (not numerically quoted)
    The informed sampling method concentrates measurements at a distance given by this radius; the paper selects the HWHM that gives the best recovery on the example, so the 2% recovery result depends on this fitted parameter.
assumptions (4)
  • standard math Compressed sensing theory: sparse signals can be recovered from incoherent subsampled measurements.
    Invoked in the abstract and methods; the core of the method.
  • domain assumption The LDOS-to-QPI relationship is a linear Fourier transform.
    Used in Methods: the problem is cast into 1D and the CS recovery is performed in Fourier space.
  • domain assumption Real QPI patterns are sparse in Fourier space.
    Stated in the abstract: "the requirement of CS is naturally fulfilled for QPI, since CS relies on sparsity in a vector domain, here given by few nonzero coefficients in Fourier space."
  • domain assumption The simulated Cu(111) surface state with point scatterers is representative of real QPI experiments.
    The demonstration and all conclusions rest on this simulation; no experimental data is provided.

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Cite this review

Pith. "Pith review of Sparse Sampling for Fast Quasiparticle Interference Mapping." pith.science (2026). https://pith.science/paper/F3LLJCDX

@misc{pith2026190801903,
  author       = {Pith},
  title        = {Pith review of: Sparse Sampling for Fast Quasiparticle Interference Mapping},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/F3LLJCDX}},
  note         = {Machine review of arXiv:1908.01903}
}
read the original abstract

Scanning tunneling microscopy (STM) is a notoriously slow technique; Data-recording is serial which renders complex measurement tasks, such as quasiparticle interference (QPI) mapping, impractical. However, QPI would provide insight into band-structure details of quantum materials which can be inaccessible to angle-resolved photoemission spectroscopy. Here we use compressed sensing (CS) to fundamentally speed-up QPI mapping. We reliably recover the QPI information from a fraction of the usual local density of state measurements. The requirement of CS is naturally fulfilled for QPI, since CS relies on sparsity in a vector domain, here given by few nonzero coefficients in Fourier space. We exemplify CS on a simulated Cu(111) surface using random sampling of constant and varying probability density. We further simplify the motion of the STM tip through an open traveling salesman's problem for greater efficiency. We expect that the implications of our CS approach will be transformative for the exploration of 2D quantum materials.

Discussion (0). Continue with ORCID to comment.

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