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arxiv: 1907.03278 · v1 · pith:2XDODGF7new · submitted 2019-07-07 · 📡 eess.SP · physics.geo-ph

Stacked autoencoders based machine learning for noise reduction and signal reconstruction in geophysical data

Debjani Bhowick , Deepak K. Gupta , Saumen Maiti , Uma Shankar This is my paper

Pith reviewed 2026-05-25 01:28 UTC · model grok-4.3

classification 📡 eess.SP physics.geo-ph
keywords autoencodersdenoisinggeophysical datamachine learningsignal reconstructionnoise reductionstacked networks
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The pith

Stacked autoencoders reconstruct clean geophysical signals from noisy inputs by learning a lower-dimensional hidden representation.

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

The paper establishes that autoencoders can be trained to output the noise-free component of geophysical data even when the input contains noise. It introduces a stacked deep autoencoder trained in two stages: first initializing weights locally with single-hidden-layer autoencoders, then optimizing the full network. This is shown to work on a basic mathematical case and multiple geophysical examples, where the output data has substantially less noise than the input. A reader would care because geophysical measurements are routinely contaminated by noise that standard filters may not fully separate from the underlying signal.

Core claim

Autoencoders project input data nonlinearly onto a lower-dimensional hidden space in which important features are highlighted; even when the input is noisy, the network can be trained so that the reconstruction step recovers the clean signal component. The stacked variant uses local pretraining on basic single-hidden-layer autoencoders to set initial weights before full-network training, and this procedure reduces noise across all examined mathematical and geophysical cases.

What carries the argument

Stacked autoencoder with two-step training, in which single-hidden-layer autoencoders first learn local weights that initialize the deeper network before joint optimization of the full model.

If this is right

  • The same two-step stacked training produces usable denoised versions of both synthetic and field geophysical datasets.
  • Feature highlighting in the hidden space improves downstream interpretation of the reconstructed signals.
  • The method operates without an explicit parametric model of the noise distribution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach may transfer to other measurement domains where signals share consistent low-dimensional structure across examples.
  • Performance could degrade if the training set lacks sufficient variety in signal patterns relative to the noise.
  • Extending the architecture depth or adding regularization terms might further separate signal from noise on larger datasets.

Load-bearing premise

The lower-dimensional representation learned from noisy data encodes the clean geophysical signal rather than a blend of signal and noise patterns.

What would settle it

Running the trained stacked autoencoder on held-out noisy geophysical traces yields outputs whose noise level is not lower than the input or whose signal features deviate from known clean reference traces.

Figures

Figures reproduced from arXiv: 1907.03278 by Debjani Bhowick, Deepak K. Gupta, Saumen Maiti, Uma Shankar.

Figure 1
Figure 1. Figure 1: Schematic structure of a traditional neural network. For [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic diagram of a denoising autoencoder showing the encoder and decoder segments. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic diagram of a stacked denoising autoencoder showing the two steps involved in the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Relative noise reduction η for the 100 noisy test samples, (b) noise-free, noisy and autoen￾coder (AE) corrected data for sample index 20 and (c) for sample index 70. A denoising autoencoder comprising 2 hidden layers with 20 neurons in each is used. functions are used for projection from the input layer to hidden layer 1 and hidden layer 1 to hidden layer 2. For obtaining the output z, linear activati… view at source ↗
Figure 5
Figure 5. Figure 5: Schematic diagram of a buried vertical cylinder, also showing some of the parameters that [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Noise-free, noisy and autoencoder (AE) corrected data for samples with index 27, 73 and 282. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: An example seismic section considered for generating the training and test samples for this [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Schematic diagram demonstrating the extraction of small image slices from a test image of [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Denoising of corrupted seismic data using a traditional deep autoencoder and a stacked deep [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Schematic diagram of an m × n image slice provided as a training sample to the denoising autoencoder. Here, the superscripts 1, 2, 3, . . ., n denote the features used for training. For the well data denoising problem considered in this paper, the features are porosity, saturation, p-wave velocity and clay content. To denoise the i th data point in the well logs, the image slice includes information of m−… view at source ↗
Figure 11
Figure 11. Figure 11: Noisefree, noisy and autoencoder (AE) corrected [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Noisefree, noisy and autoencoder (AE) corrected porosity values [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Noisefree, noisy and autoencoder (AE) corrected [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
read the original abstract

Autoencoders are neural network formulations where the input and output of the network are identical and the goal is to identify the hidden representation in the provided datasets. Generally, autoencoders project the data nonlinearly onto a lower dimensional hidden space, where the important features get highlighted and interpretation of the data becomes easier. Recent studies have shown that even in the presence of noise in the input data, autoencoders can be trained to reconstruct the noisefree component of the data from the reduced-dimensional hidden space. In this paper, we explore the application of autoencoders within the scope of denoising geophysical datasets using a data-driven methodology. The autoencoder formulation is discussed, and a stacked variant of deep autoencoders is proposed. The proposed method involves locally training the weights first using basic autoencoders, each comprising a single hidden layer. Using these initialized weights as starting points in the optimization model, the full autoencoder network is then trained in the second step. The applicability of denoising autoencoders has been demonstrated on a basic mathematical example and several geophysical examples. For all the cases, autoencoders are found to significantly reduce the noise in the input data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a two-stage stacked autoencoder architecture (local pre-training of single-hidden-layer autoencoders followed by end-to-end fine-tuning) for denoising geophysical signals. It applies the method to a synthetic mathematical example and several geophysical datasets, asserting that the approach significantly reduces noise in the input data for all examined cases.

Significance. If the central claim were supported by objective metrics and independent validation, the work would offer a practical data-driven alternative for noise suppression in geophysical signal processing. The two-stage training is a standard initialization technique, but its utility here depends on demonstrating genuine signal recovery rather than generic compression.

major comments (3)
  1. [Abstract] Abstract: the assertion that autoencoders 'significantly reduce the noise' for all cases supplies no quantitative metrics (SNR improvement, MSE, or similar), error bars, or baseline comparisons, leaving the central empirical claim unsupported.
  2. [Geophysical examples] Geophysical examples section: without ground-truth clean signals, visual inspection cannot confirm that the hidden representation isolates the geophysical signal rather than performing dimensionality-reduction smoothing; any sufficiently compressive autoencoder could yield comparable visual results.
  3. [Method and results] Method and results: training and evaluation are performed on the identical noisy observations, so reported reconstruction quality is a fitted quantity whose value depends on architecture and optimization choices rather than an independent test of signal recovery.
minor comments (2)
  1. [Method] The description of the two-stage training procedure would benefit from an explicit diagram or pseudocode to clarify the local pre-training versus global fine-tuning steps.
  2. [Autoencoder formulation] Notation for encoder/decoder weights and hidden-layer dimensions is introduced without a consolidated table, making it harder to reproduce the exact architectures used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below, indicating where revisions will be incorporated to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that autoencoders 'significantly reduce the noise' for all cases supplies no quantitative metrics (SNR improvement, MSE, or similar), error bars, or baseline comparisons, leaving the central empirical claim unsupported.

    Authors: The abstract condenses the visual evidence from the figures. We agree that quantitative support would improve clarity. In revision we will insert SNR and MSE values (with the synthetic mathematical example, where a clean reference is available) and will explicitly qualify the real-data cases as relying on visual assessment. revision: yes

  2. Referee: [Geophysical examples] Geophysical examples section: without ground-truth clean signals, visual inspection cannot confirm that the hidden representation isolates the geophysical signal rather than performing dimensionality-reduction smoothing; any sufficiently compressive autoencoder could yield comparable visual results.

    Authors: Ground-truth clean signals are unavailable for the field geophysical datasets, a common constraint in the domain. The two-stage training procedure is intended to encourage recovery of structured signal components rather than generic smoothing. We will add side-by-side comparisons against standard denoising baselines (e.g., wavelet thresholding) to provide additional evidence that the learned representation offers advantages beyond simple compression. revision: yes

  3. Referee: [Method and results] Method and results: training and evaluation are performed on the identical noisy observations, so reported reconstruction quality is a fitted quantity whose value depends on architecture and optimization choices rather than an independent test of signal recovery.

    Authors: Autoencoder denoising is unsupervised by design; the network is trained to reconstruct its noisy input through a bottleneck. For the synthetic example an independent clean reference exists and will be used for explicit error quantification. We will revise the text to state this distinction clearly and, where data volume permits, introduce a hold-out subset for the synthetic case to illustrate generalization. revision: partial

Circularity Check

0 steps flagged

No circularity; empirical demonstration on provided examples is self-contained

full rationale

The paper describes a data-driven application of stacked autoencoders trained end-to-end on the input geophysical datasets themselves to produce reconstructions. No first-principles derivation, uniqueness theorem, or parameter-free prediction is claimed that reduces by construction to the training inputs. Results are presented as empirical demonstrations on a mathematical example and geophysical cases, which constitutes standard supervised evaluation rather than a circular reduction. No self-citations or ansatzes are invoked as load-bearing steps in the provided text.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The method rests on standard neural-network assumptions plus hyperparameters chosen during training. No new physical entities are postulated.

free parameters (2)
  • network depth and hidden-layer widths
    Chosen to match data dimensionality and to allow a bottleneck representation.
  • learning rate, batch size, and number of epochs
    Tuned so that the optimization converges on the given datasets.
axioms (1)
  • domain assumption A neural network with a bottleneck layer can separate repeatable signal structure from uncorrelated noise when trained on many examples.
    Invoked when the authors state that the autoencoder reconstructs the noisefree component.

pith-pipeline@v0.9.0 · 5750 in / 1269 out tokens · 26870 ms · 2026-05-25T01:28:32.463367+00:00 · methodology

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