Signal denoising based on the Schr\"odinger operator's eigenspectrum and a curvature constraint

Peihao Li; Taous Meriem Laleg-Kirati

REVIEW 4 major objections 7 minor 18 references

Signal denoising based on the Schr\"odinger operator's eigenspectrum and a curvature constraint

T0 review · 4 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A curvature penalty lets Schrödinger-operator denoising preserve pulse peaks without requiring peak locations or noise-region priors.

desk verdict C-SCSA is a plausible incremental extension of the authors' SCSA denoiser, but the curvature-penalty justification does not actually transfer from the noisy input to the reconstruction, so the peak-preservation claim should be read as an empirical observation, not a proven guarantee. read the letter →

arxiv 1908.07758 v1 pith:FB6N6CQ4 submitted 2019-08-21 eess.SP

Peihao Li , Taous Meriem Laleg-Kirati This is my paper · ORCID

classification eess.SP

keywords signaldenoisingSchrödingeroperatorsemi-classicalanalysiscurvatureconstraintpeakpreservationeigenvaluespectrumECGsemiclassicalparameter

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

This paper tries to establish that a denoising method built on the Schrödinger operator's eigenspectrum can be made general by adding a curvature constraint. Earlier SCSA denoising required knowing where the signal peaks are and where noise dominates, which restricted it to specialized applications such as magnetic resonance spectroscopy. The proposed C-SCSA replaces that prior knowledge with a penalty on the wiggliness of the reconstructed signal, and the reported experiments indicate that it preserves peak height and width better than Savitzky-Golay, wavelet, and EMD baselines while delivering competitive signal-to-noise ratios. If correct, this offers a peak-preserving denoising strategy for pulse-shaped and slowly varying biomedical signals that needs no manual peak annotation.

What carries the argument

The central object is the Schrödinger operator $-h^2 \frac{d^2\psi}{dt^2} - y(t)\psi = \lambda\psi$, with the noisy signal acting as the potential. Its negative eigenvalues $\lambda_{nh} = -\kappa_{nh}^2$ and the associated $L^2$-normalized eigenfunctions $\psi_{nh}$ are used to reconstruct the signal as $y_h(t) = 4h \sum_{n=1}^{N_h} \kappa_{nh} \psi_{nh}^2(t)$. The semiclassical parameter $h$ controls how many eigenfunctions are retained, and the curvature constraint $k(t) = |y_h''(t)|/(1 + y_h'(t)^2)^{3/2}$ is the mechanism that selects $h$. The load-bearing identity is Proposition 1's formula, which gives the expected curvature of adjacent differences as an integral that grows with the noise variance, thereby connecting larger noise to larger curvature and motivating the penalty term in the cost function.

What would settle it

Generate a signal with sharp true spikes whose curvature is comparable to or larger than the curvature of the added noise, run C-SCSA at noise levels from 1% to 12%, and measure peak height and width relative errors. If the errors are as large as those of Savitzky-Golay filtering, the claim that C-SCSA guarantees peak preservation fails. Alternatively, compare the curvature of the chosen $y_h$ to the curvature of the true signal: if the reconstructed curvature is systematically lower for signals with genuinely high-curvature features, the curvature penalty is over-smoothing beyond noise removal.

Watch

Extended reading notes

Core claim

The central claim is that selecting the semiclassical parameter $h$ by minimizing a cost function that combines fidelity to the noisy signal with a curvature penalty on the reconstruction yields a denoiser that removes noise without flattening peaks. Specifically, the paper defines $J = \|y_\delta - y_h\|_2^2 + \mu \int |k(t)|\,dt$, where $k(t)$ is the curvature of the reconstructed signal, and then scans $h$ to minimize this cost. The supporting theoretical result, Proposition 1, derives an expression for the expected curvature of adjacent differences in the noisy signal and shows that this expectation increases with the noise variance; the paper uses this to justify penalizing curvature as a noise-reduction mechanism. Numerically, C-SCSA reports lower peak-height and peak-width relative errors than the comparison methods on single Gaussian peaks, and higher or comparable post-denoising SNR on simulated multi-peak signals, real-noise ECG records, and several standard test signals, especially when the signal is regular and slowly varying.

Load-bearing premise

The proof shows that adjacent differences in the noisy input have larger expected curvature when noise increases, but the algorithm actually penalizes the curvature of the reconstructed signal; the paper does not prove that these two curvatures are equivalent or that minimizing the latter removes the former.

Editorial extensions

If this is right

C-SCSA can be applied to pulse-shaped signals without needing to locate peaks or identify noise-dominant intervals, unlike the earlier α-SCSA method.
On single Gaussian peaks with 1–12% Gaussian noise, C-SCSA reports lower peak-height and peak-width relative errors than EMD-IT, Savitzky-Golay, and wavelet denoising.
On multi-peak simulated signals and real-noise ECG records from the MIT-BIH database, C-SCSA achieves SNR after denoising that is competitive with or better than Savitzky-Golay and EMD-IT, and comparable to the wavelet method.
On piecewise-regular, Doppler, blocks, bumps, and sing test signals, C-SCSA outperforms EMD-IT and Savitzky-Golay for regular and slowly varying cases, and remains effective across sampling frequencies from 256 to 2048 samples.
Because the cost function operates on the whole signal, C-SCSA extends SCSA-based denoising beyond magnetic resonance spectroscopy to a broader class of biomedical and spectral signals.

Reading between the lines

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

The curvature-based rule suggests a general principle for spectral denoising: choose the decomposition threshold by minimizing fidelity plus a geometric regularity term, which could also be applied to wavelet coefficient selection or EMD interval thresholding.
Proposition 1's relation between adjacent-difference curvature and noise variance could be inverted to estimate the noise level from a single noisy record, allowing the smoothing parameter $\mu$ to be set automatically rather than by an order-of-magnitude scan.
The method's dependence on reconstruction curvature implies it may over-smooth signals whose true features have curvature comparable to noise, such as very sharp spikes or edges; testing on such signals would reveal the boundary of the peak-preservation claim.
Viewing the curvature penalty as a form of total-variation or mean-curvature flow could connect C-SCSA to nonlinear diffusion denoising and potentially yield convergence guarantees that the paper does not provide.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a useful incremental paper, not a breakthrough. The new bit is C-SCSA—using a curvature penalty to pick the semi-classical parameter h, instead of the peak-localization and noise-region priors that α-SCSA needed. That is a real practical improvement for pulse-shaped biomedical signals, and the paper backs it with comparisons against Savitzky-Golay, wavelet, and EMD on Gaussian peaks, ECG with real MIT-BIH noise, and several benchmark signals at different sampling rates. The derivation of Proposition 1 checks out: under the zero-mean jointly Gaussian model for adjacent differences, the expected curvature of the noisy input increases with noise variance. The citation pattern is fine too—the authors lean on their own prior SCSA work, which is expected when the whole method builds on it.

The main soft spot is exactly the one flagged in the stress test. The theorem is about curvature of the noisy input yδ, while the penalty in Eq. (10) is applied to the SCSA reconstruction y_h. Penalizing y_h's curvature does not follow from the noise-driven increase in yδ's curvature. Peaks are high-curvature features, so a curvature penalty can in principle suppress them; the "guarantee" of peak preservation is not established by the proposition. The simulation evidence suggests the method preserves peaks in the tested cases, but that is an empirical claim, and the paper should say so. This is a genuine gap, but not fatal to the paper's practical value: the penalty can be read as a standard smoothness prior, and the empirical results are what they are.

The other concerns are smaller. Parameters for C-SCSA and the baselines are tuned at 5% noise using the true clean signal, then fixed across noise levels; that is acceptable for a controlled comparison, but the reported advantage is an upper bound on what users should expect. There are no error bars on the peak-preservation curves in Fig. 3, and no code, so reproducibility is limited. SCSA is introduced for positive potentials, and ECG records contain negative deflections; the paper never says how this is handled. That last point needs to be addressed in revision.

Who is this for? Someone working on SCSA or peak-preserving denoising of MRS/ECG/pulse signals will find the algorithm and comparison useful. It deserves a serious referee, but with the expectation of major revision: reframe the theoretical claim, address the positivity issue, release code or at least detailed pseudo-code, and report variance over noise realizations.

Referee Report

4 major / 7 minor

Summary. The manuscript proposes C-SCSA, a denoising method that augments semi-classical signal analysis (SCSA) with a curvature penalty. Section 3 defines the cost function Jbar = sum_i [y_delta(t_i) - y_h(t_i)]^2 + mu sum_i k(t_i), where k(t_i) is the curvature of the SCSA reconstruction y_h, and Proposition 1 computes the expected curvature of adjacent differences of the noisy input under a zero-mean jointly Gaussian model, showing that this expectation increases with the noise variance. The algorithm then scans the semi-classical parameter h to minimize Jbar. Section 4 evaluates C-SCSA against Savitzky-Golay, wavelet, and EMD-IT denoising on single- and multi-peak Gaussian signals, ECG records corrupted with real noise from the MIT-BIH database, and standard test signals (Doppler, piecewise-regular, blocks, bumps) at multiple noise levels and sampling frequencies. The paper claims that C-SCSA preserves peak height and width and outperforms or matches the baselines.

Significance. The paper addresses a practically relevant problem: denoising pulse-shaped signals without peak-localization priors. The C-SCSA cost function is a reasonable extension of SCSA, and the simulation protocol is detailed, including multiple signals, noise levels, sampling frequencies, and a real-noise ECG test against three baselines. Proposition 1 is a nontrivial calculation, and the appendix derivation is internally consistent. However, the central theoretical link from noise-driven curvature of the input to a penalty on the reconstruction's curvature is not established, and the parameter selection uses oracle knowledge of the clean signal. As presented, the claimed guarantee of peak preservation is not supported, so the significance is conditional on additional analysis and validation.

major comments (4)

[Section 3, Eqs. (5)-(10) and Proposition 1] The theoretical support for the curvature penalty is derived for the adjacent differences x_m and w_m of the noisy input y_delta under a zero-mean jointly Gaussian model (Eq. 7), but the penalty in Eq. (10) is applied to the curvature k(t_i) of the SCSA reconstruction y_h. The paper does not provide a lemma or estimate showing that penalizing the reconstruction's curvature is equivalent to, or even correlated with, reducing the input curvature caused by noise. Because signal peaks have high curvature, the penalty can suppress the very features the method claims to preserve; therefore the statement in Section 5 that C-SCSA 'guarantees the peaks are well preserved' is not justified by Proposition 1. Either supply a transfer argument relating curvature of y_h to noise in y_delta, or reword the claim and support peak preservation empirically over a range of mu and h.
[Section 4.2, parameter selection paragraph] The description 'we optimize each method's parameter at noise level 5%, where we iteratively optimize its parameter using the noisy signal and true signal' means that mu (and h) for C-SCSA, as well as baseline parameters, are chosen with the true clean signal. This is oracle tuning: it does not correspond to a deployable procedure when the clean signal is unknown, and it weakens the claim that C-SCSA does not need to locate signal peaks or know the noise level. The paper should either specify a fully data-driven selection rule for mu (the current rule involving max{|y_delta|} * sum k(i) * 10^nu leaves nu unspecified) or present the comparison as an oracle-parameter study and discuss behavior when parameters are selected without the clean signal.
[Section 4.3, ECG experiments] SCSA is defined for a real positive potential y(t) (Section 2.1 and Eq. 2), yet the ECG records shown in Fig. 5 have amplitudes ranging from about -200 to 400, i.e., they contain negative values. The paper never states how the potential is made positive before computing the Schrodinger spectrum. If a baseline shift is applied, it should be described and its effect on the reported SNR improvements quantified; without this, the eigenvalue problem and the reconstruction in Eq. (1) are not well defined for these signals.
[Section 4.2, Fig. 3] The peak-preservation experiment is performed on a single simulated Gaussian peak, and no repeated noise realizations or error bars are reported for the peak-height and peak-width relative errors; the text elsewhere reports ensemble averages over 90 realizations. Consequently, the claimed superiority of C-SCSA in peak preservation could reflect a single noise draw rather than a stable advantage. Repeating the experiment over multiple noise realizations and reporting mean plus or minus standard deviation (or box plots) is necessary to support the central peak-preserving claim.

minor comments (7)

[Eq. (10)] The summation lower limit is written as 'i = i' and should be 'i = 1'.
[Eq. (4)] The sign of the alpha * |SNR_yh| term in the alpha-SCSA cost appears inconsistent with minimization: if a larger SNR is desirable, adding a positive SNR term increases the cost for better reconstructions. Clarify whether the term should be negative or should be alpha / SNR_yh.
[Fig. 4 caption] The caption states that the noise level ranges between 0.1% and 15% with interval 0.1%, but the horizontal axis shows values from 1 to 10, and the preceding paragraph describes a 1% to 12% range. Please make the range and units consistent.
[Figs. 6 and 7 captions] The x-axis labels are inconsistent with the experiments: Fig. 6 labels the x-axis 'Noise Level (%)' while the text indicates noise levels 7%-15%, and Fig. 7 panels show both 'Noise Level (%)' and 'Number of Samples' on the x-axis although the text describes a sampling-frequency experiment. Correct all axis labels, legends, and figure cross-references.
[Fig. 8 caption] Both panels (b) and (c) in the caption are described as 'C-SCSA denoising', but the surrounding text states that alpha-SCSA failed on the piecewise-regular signal. Clarify which panel shows alpha-SCSA and which shows C-SCSA.
[Section 4.4, cross-references] The text cites 'Fig. 7(a) and (d)' and 'Fig. 8(a)(b)(c)(d)' in a way that does not match the figures' content; all figure cross-references should be checked and updated.
[Section 4.2, Savitzky-Golay settings] The Savitzky-Golay parameters differ between Fig. 3 (window 29, degree 4) and Fig. 4 (filter length 17, order 4); the manuscript should explain why different settings are used in the two experiments or use a single configuration.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: C-SCSA is validated on external benchmarks; the curvature-penalty justification is a missing transfer step, not a circular reduction.

full rationale

The paper's claimed contribution is the C-SCSA cost function, Eq. (10): J-bar = sum_i [y_delta(t_i) - y_h(t_i)]^2 + mu sum_i k(t_i), where y_h is the SCSA reconstruction from Eqs. (1)-(2). The SCSA reconstruction itself is imported from the authors' prior work, but that prior work is an independent published spectral-theoretic result with stated assumptions, not a parameter fitted to the present target data. The denoising claims are tested against external benchmarks: synthetic Gaussian peaks with known clean signals, MIT-BIH ECG records with real noise, and standard test signals (Doppler, Blocks, Bumps, Piecewise-Regular, Sing). No fitted parameter or subset of the target data is renamed as a prediction; the reported SNRs and MSEs are measured against known ground truth. The one theoretical result, Proposition 1 (Eq. 9), derives that the expected curvature of adjacent differences of the noisy input y_delta increases with noise variance. The algorithm, however, penalizes the curvature of the reconstructed signal y_h. No lemma transfers the Proposition's monotonicity from the input's adjacent differences to the curvature of y_h, so the link between the theorem and the cost function is assumed rather than derived. This is a logical gap or correctness risk, not a circular reduction: the penalty is not defined in terms of the quantity being predicted, and the 'guarantee' of peak preservation in the abstract and conclusion is an empirical observation from Fig. 3 rather than a theorem derived from the paper's own inputs. The parameter selection for baselines is a tuning/evaluation issue, not a circularity in the derivation chain. Accordingly, no circular step is present; the score is 0.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on three kinds of unpaid inputs: the prior SCSA theory supplied by the authors' own references, which provides the reconstruction formula and the noise-versus-detail ordering of eigenfunctions; the Gaussian model for adjacent differences used in Proposition 1; and the tunable parameters h and μ that are scanned per signal. The paper reports no code or exact search grids, so the specific numbers in the figures are not independently recoverable from the text. The method introduces no new physical entities, but the application to ECG signals with negative amplitudes presupposes a positivity handling that is not described.

free parameters (2)

Semi-classical parameter h = No single optimum reported; scanned or iteratively decreased to minimize the cost function, with example values 100…
Controls the number of negative eigenfunctions retained and therefore how much noise is reconstructed. It is chosen by iterative scanning in every experiment, so the reported results depend on this manual selection.
Curvature penalty weight μ = Signal-dependent; set by max{|yδ(ti)|} Σk(i) · 10^ν with ν∈Z, and refined by scanning per signal and noise level
Balances fidelity to the noisy signal against smoothness in the cost function. The paper gives no principled rule for choosing ν, and the simulations further tune μ using the true clean signal at 5% noise.

assumptions (5)

domain assumption The Schrödinger operator reconstruction formula y_h = 4h Σ κ_nh ψ_nh^2 converges to the signal as h tends to zero, and higher-order eigenfunctions mainly reconstruct noise.
Borrowed from the authors' prior SCSA theory (references [1] and [2]) without proof. This spectral decomposition property is the foundation of the denoising mechanism and is not re-derived here.
domain assumption The input signal y(t) is positive, as required for the SCSA reconstruction formula in Eq. (1).
Section 2.1 states that SCSA decomposes a real positive signal, but Section 4.3 applies the method to ECG signals with negative amplitudes in Fig. 5 without describing any positivity shift or preprocessing step.
domain assumption Adjacent differences x_m = y_{m+1} - y_m and w_m = y_m - y_{m-1} are jointly Gaussian, zero-mean, with equal variance σ_m^2 and small correlation ρ_m.
Stated in Eq. (7) and used in Proposition 1. This is an approximation for real signals and is not validated against the test signals used in the simulations.
domain assumption Noise variance in homogeneous signal regions satisfies σ_m^2 ≈ 2 σ_noise^2.
Used to argue that increasing noise increases the expected curvature. It is only valid where the underlying signal is locally flat, which is not true at peaks and sharp transitions.
domain assumption The finite-difference approximation of curvature in Eq. (8) adequately represents the continuous curvature defined in Eq. (6).
Used without error analysis. It is standard for smooth, well-sampled signals but is not quantified for the multi-peak and ECG signals considered later.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Signal denoising based on the Schr\"odinger operator's eigenspectrum and a curvature constraint." pith.science (2026). https://pith.science/paper/FB6N6CQ4

@misc{pith2026190807758,
  author       = {Pith},
  title        = {Pith review of: Signal denoising based on the Schr\"odinger operator's eigenspectrum and a curvature constraint},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FB6N6CQ4}},
  note         = {Machine review of arXiv:1908.07758}
}

read the original abstract

Recently, a new Signal processing method, named Semi-Classical Signal Analysis (SCSA), has been proposed for denoising Magnetic Resonance Spectroscopy (MRS) signals. It is based on the Schr\"odinger Operator's eigenspectrum. It allows an efficient noise reduction while preserving MRS signal's peaks. In this paper, we propose to extend this approach to different signals, in particular pulse shaped signals, by including an optimization that considers curvature constraints. The performance of the method is measured by analyzing noisy signal data and comparing with other denoising methods. Results indicate that the proposed method not only produces good denoising performance but also guarantees the peaks are well preserved in the denoising process.

Figures

Figures reproduced from arXiv: 1908.07758 by the authors.

**Figure 1.** Nh is the number of negative eigenfunctions and h is a positive parameter known as the semi-classical constant. It is found that when h tends to zero, the reconstructed spectrum yh converges to the true spectrum y. This matches the semi-classical properties of the Schrödinger operator where the number of negative eigenvalues thus the number of corresponding eigenfunctions increases when h decreases. One of the impor… view at source ↗

**Figure 1.** SCSA method. (a) Input Signal with 4 major peaks (b) Squared eigenfunctions of the signal, with only few of them (4 in this case) corresponding to the major peaks and rest of them explaining the details 2.2 SCSA for signal denoising Now, let’s consider the following noisy signal yδ(t) = y(t) + n(t), (3) where y(t) is the noiseless signal and n(t) is the additive noise. The aim of digital signal denoising is to produ… view at source ↗

**Figure 2.** A selection of optimal h has to be made in order to separate noise from the original signal. In simulation, h is initiated at a relatively small value at first and then gradually increased to discard the noise part. One can infer that the choice of the stop criterion is critical, since it sets the optimum h value, which leads to a reliable signal reconstruction and therefore to an accurate data analysis. It is found… view at source ↗

Figures from the paper (8 more)

**Figure 2.** Figure 2: SCSA’s application in signal denoising. Input signal with noise(in blue), SCSA spectrum (in red) and residual (in green) (a) Small Nh value, not capable of reconstructing the signal. (b)(c) Nh increases, the peaks of the signals are recovered, without recovering the r…

**Figure 3.** Figure 3: Peak preserving performance for single Gaussian peak . (a) Peak height preserving performance (b) Peak width preserving performance (Noise level ranges between 1% and 12% (with interval 0.5%) as shown in the horizontal axis). performance. Denoising Performance and comp…

**Figure 4.** Figure 4: Quantitative Denoising Performance of Different Noise Levels. Noise level ranges between 0.1% and 15% (with interval 0.1%) as shown in the horizontal axis. (a) Mean Squared error . (b) SNR (dB). Both wavelet and Savitzky-Golay methods are optimized as described. sym4 b…

**Figure 5.** Figure 5: Enhancement for ECG signals. From top to bottom: (a) Real noise plot, with muscle artifacts (in red) and electrode motion artifacts (in blue). (b) Contaminated ECG signal (SNR = 9.0678 dB). (c) SCSA denoising method (SNR = 11.4315 dB). In the last graphs, the reconstru…

**Figure 6.** Figure 6: Denoising performance for different types of signals . (a)(b)(c)(d) SCSA, EMD-Interval thresholding and Savitzky Golay filter denoising performance under different noise level (Noise level ranges between 7%-15% (with interval 0.1%) as shown in the horizontal axis). 17 …

**Figure 7.** Figure 7: Denoising performance for different sampling frequencies . (a)(b)(c)(d) SCSA, EMD-Interval thresholding and Savitzky Golay filter denoising performance under 10% noise level. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

**Figure 8.** Figure 8: α-SCSA and C-SCSA denoising implementation of the piecewiseregular signal. From top to bottom: (a) Clean signal (in red) and noisy signal (in blue). (b) Results of the C-SCSA denoising with clean signal (in red) and denoised signal (in blue) (SNR = 30.2657 dB). (c) Re…

**Figure 9.** Figure 9: Signals used for validation of different denoising methods. [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages

[1]

Spectral data de-noising using semi- classical signal analysis: application to localized MRS

T. M. Laleg-Kirati, J. Zhang, E. Achten, and H. Serrai, "Spectral data de-noising using semi- classical signal analysis: application to localized MRS”, NMR Biomed, vol.29, pp. 1477-1485, 2016

work page 2016
[2]

Semi-classical signal analysis

T. M. Laleg-Kirati, E. Crépeau, M. Sorine, "Semi-classical signal analysis”, Math. Control Signals Syst, 2013

work page 2013
[3]

Arterial blood pressure analysis based on scattering transform II

T. M. Laleg-Kirati, Medigue. C, Cottin F, Sorine. M, "Arterial blood pressure analysis based on scattering transform II”, Proceedings of EMBC Sciences and Technologies for Health, Lyon, France, pp. 3618-3629, 2007

work page 2007
[4]

Validation of a semi-classical signal analysis method for stroke volume variation assessment: A comparison with the PiCCO technique Ann Biomed Eng

T. M. Laleg-Kirati, C. Medigue, Y. Papelier, et al, "Validation of a semi-classical signal analysis method for stroke volume variation assessment: A comparison with the PiCCO technique Ann Biomed Eng”, vol.38, pp. 3618-3629, 2010

work page 2010
[5]

Residual Water Suppression Using the Squared Eigenfunctions of the Schrodinger Operator

A. Chahid, S. Bhaduri, M. Maoui, R Achten H. Serrai and T.M. Laleg-Kirati, "Residual Water Suppression Using the Squared Eigenfunctions of the Schrodinger Operator ", IEEE access, Vol. 9, 69126–69137, 2019. 24

work page 2019
[6]

Feature Generation and Di- mensionality Reduction using the Discrete Spectrum of the Schrödinger Operator for Epileptic Spikes Detection

A. Chahid,T. N. Alotaiby, S. Alshebeili and T-M Laleg-Kirati, "Feature Generation and Di- mensionality Reduction using the Discrete Spectrum of the Schrödinger Operator for Epileptic Spikes Detection", In Proceeding IEEE EMBC July 2019

work page 2019
[7]

Width Based Quantitation of Chromatographic Peaks: Principles and Principal Characteristics

A. F. Kadjo, P. K. Dasgupta, J. Su, S. Y. Liu, and K. G. Kraiczek, "Width Based Quantitation of Chromatographic Peaks: Principles and Principal Characteristics”, Analytical Chemistry, vol. 89 no.7, pp. 3884-3892, 2017

work page 2017
[8]

Hastie, R

T. Hastie, R. Tibshirani, Generalized Additive Models, Chapman and Hall, 1990

work page 1990

Show all 18 references

[9]

Denoising an image by denoising its curvature image

M. Bertalmío, S. Levine, "Denoising an image by denoising its curvature image”, SIAM J. Imag. Sci., vol. 7, no. 2, pp. 187-201, 2014

2014
[10]

High frequency noise removal from ECG using moving average ﬁlters

V. Pandey and V. K. Giri, "High frequency noise removal from ECG using moving average ﬁlters”, International Conference on Emerging Trends in Electrical Electronics & Sustainable Energy Systems (ICETEESES), Sultanpur, pp. 191-195, 2016

2016
[11]

Review and comparison of smoothing algorithms for one- dimensional data noise reduction

P. Kowalski and R. Smyk, "Review and comparison of smoothing algorithms for one- dimensional data noise reduction”, 2018 International Interdisciplinary PhD Workshop (IIPhDW), Swinoujście, pp. 277-281, 2018

2018
[12]

Smoothing and Diﬀerentiation of Data by Simpliﬁed Least Squares Procedures

Abraham. Savitzky and M. J. E. Golay, "Smoothing and Diﬀerentiation of Data by Simpliﬁed Least Squares Procedures”, Analytical Chemistry, vol. 36, no. 8, pp. 1627-1639, 1964

1964
[13]

Application of adaptive Savitzky–Golay ﬁlter for EEG signal processing

D. Acharya, A. Rani, S. Agarwal, V. Singh, "Application of adaptive Savitzky–Golay ﬁlter for EEG signal processing”, Perspectives in Science, vol. 8, pp. 677-679, 2016

2016
[14]

Nonlineardiﬀusionﬁlteringforpeak-preservingsmoothingofaspectrum signal

Y.Li, Y.Ding, T.Li, "Nonlineardiﬀusionﬁlteringforpeak-preservingsmoothingofaspectrum signal”, Chemometrics and Intelligent Laboratory Systems, vol. 156, pp. 157-165, 2016

2016
[15]

Optimizing Savitzky-Golay parameters for improving spectral resolution and quantiﬁcation in infrared spectroscopy

B. Zimmermann, A. Kohler, "Optimizing Savitzky-Golay parameters for improving spectral resolution and quantiﬁcation in infrared spectroscopy”, Appl. Spectrosc, vol. 67, pp. 892-902, 2013. 25

2013
[16]

Optimal selection of wavelet basis function applied to ECG signal denoising

B. N. Singh, A. K. Tiwari, "Optimal selection of wavelet basis function applied to ECG signal denoising”, Digital Signal Processing, vol. 16, no. 3, pp. 275-287, 2006

2006
[17]

PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals

A. L. Goldberger, L. A. N. Amaral, L. Glass, J. M. Hausdorﬀ, P. C. Ivanov, R. G. Mark, J. E. Mietus, G. B. Moody, C. K. Peng, H. E. Stanley, "PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals", vol. 101, no. 23, pp....

2000
[18]

Development of EMD-Based Denoising Methods Inspired by Wavelet Thresholding,

Y. Kopsinis and S. McLaughlin, "Development of EMD-Based Denoising Methods Inspired by Wavelet Thresholding," IEEE Transactions on Signal Processing, vol. 57, no. 4, pp. 1351-1362, April 2009. 26

2009

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Spectral data de-noising using semi- classical signal analysis: application to localized MRS

T. M. Laleg-Kirati, J. Zhang, E. Achten, and H. Serrai, "Spectral data de-noising using semi- classical signal analysis: application to localized MRS”, NMR Biomed, vol.29, pp. 1477-1485, 2016

work page 2016

[2] [2]

Semi-classical signal analysis

T. M. Laleg-Kirati, E. Crépeau, M. Sorine, "Semi-classical signal analysis”, Math. Control Signals Syst, 2013

work page 2013

[3] [3]

Arterial blood pressure analysis based on scattering transform II

T. M. Laleg-Kirati, Medigue. C, Cottin F, Sorine. M, "Arterial blood pressure analysis based on scattering transform II”, Proceedings of EMBC Sciences and Technologies for Health, Lyon, France, pp. 3618-3629, 2007

work page 2007

[4] [4]

Validation of a semi-classical signal analysis method for stroke volume variation assessment: A comparison with the PiCCO technique Ann Biomed Eng

T. M. Laleg-Kirati, C. Medigue, Y. Papelier, et al, "Validation of a semi-classical signal analysis method for stroke volume variation assessment: A comparison with the PiCCO technique Ann Biomed Eng”, vol.38, pp. 3618-3629, 2010

work page 2010

[5] [5]

Residual Water Suppression Using the Squared Eigenfunctions of the Schrodinger Operator

A. Chahid, S. Bhaduri, M. Maoui, R Achten H. Serrai and T.M. Laleg-Kirati, "Residual Water Suppression Using the Squared Eigenfunctions of the Schrodinger Operator ", IEEE access, Vol. 9, 69126–69137, 2019. 24

work page 2019

[6] [6]

Feature Generation and Di- mensionality Reduction using the Discrete Spectrum of the Schrödinger Operator for Epileptic Spikes Detection

A. Chahid,T. N. Alotaiby, S. Alshebeili and T-M Laleg-Kirati, "Feature Generation and Di- mensionality Reduction using the Discrete Spectrum of the Schrödinger Operator for Epileptic Spikes Detection", In Proceeding IEEE EMBC July 2019

work page 2019

[7] [7]

Width Based Quantitation of Chromatographic Peaks: Principles and Principal Characteristics

A. F. Kadjo, P. K. Dasgupta, J. Su, S. Y. Liu, and K. G. Kraiczek, "Width Based Quantitation of Chromatographic Peaks: Principles and Principal Characteristics”, Analytical Chemistry, vol. 89 no.7, pp. 3884-3892, 2017

work page 2017

[8] [8]

Hastie, R

T. Hastie, R. Tibshirani, Generalized Additive Models, Chapman and Hall, 1990

work page 1990