arxiv: 2604.26669 · v1 · submitted 2026-04-29 · 💻 cs.SD · math.OC

Recognition: unknown

Full band denoising of room impulse response in the wavelet domain with dictionary learning

Th\'eophile Dupr\'e , Romain Couderc , Miguel Moleron , Axel Coulon , R\'emy Bruno , Arnaud Laborie

Authors on Pith no claims yet

Pith reviewed 2026-05-07 10:37 UTC · model grok-4.3

classification 💻 cs.SD math.OC

keywords room impulse responsewavelet denoisingdictionary learninglow-frequency denoisingacoustic parameter estimationexponential decay modelsparse representation

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The pith

Sparse dictionary learning on wavelet approximation coefficients enables full-band denoising of room impulse responses.

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

Conventional wavelet denoising thresholds only the detail coefficients and leaves low-frequency content noisy. This paper adds a post-processing step that applies sparse dictionary learning to the approximation coefficients. The learning uses a time-varying error tolerance drawn from an exponential decay envelope that tracks local signal-to-noise ratio. Tests on both synthetic and measured responses show cleaner low-frequency bands and more accurate recovery of acoustic parameters such as decay time.

Core claim

By extending wavelet denoising to approximation coefficients through sparse dictionary learning with reconstruction accuracy adapted by an exponential decay envelope model according to local signal-to-noise ratio, the method achieves full-band denoising that outperforms standard thresholding on synthetic and measured room impulse responses and yields improved estimates of acoustic parameters.

What carries the argument

Sparse dictionary learning on wavelet approximation coefficients controlled by a time-varying error tolerance from an exponential decay envelope model.

If this is right

Low-frequency content of room impulse responses is denoised more effectively than with detail-coefficient thresholding alone.
Estimates of acoustic parameters such as decay time become more accurate for both synthetic and measured data.
The approach functions as a post-processing module compatible with existing wavelet pipelines.
Denoising extends across the full frequency band rather than stopping at high frequencies.

Where Pith is reading between the lines

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

The method could reduce the number of repeated measurements needed in noisy environments by improving single-shot recovery of reverberation details.
Similar envelope-driven tolerance adaptation might apply to other decaying signals such as seismic traces or audio decays.
Integration with multi-channel or higher-order ambisonic responses could extend the gains to spatial audio processing.
If the exponential envelope fits poorly in some rooms, residual artifacts may appear in the low-frequency tail.

Load-bearing premise

An exponential decay envelope model can reliably set reconstruction accuracy for approximation coefficients according to local signal-to-noise ratio without adding bias or artifacts.

What would settle it

A direct comparison on measured room impulse responses in which the proposed method produces decay-time estimates no more accurate than those from standard wavelet thresholding.

read the original abstract

Conventional wavelet-domain methods for room impulse response denoising rely on thresholding detail coefficients, which is unsuited for low frequencies. In this work, we introduce a wavelet-based post-processing algorithm that extends denoising to approximation coefficients by means of sparse dictionary learning with a time-varying error tolerance. The proposed method leverages an exponential decay envelope model to adapt reconstruction accuracy according to the local signal-to-noise ratio. This approach significantly improves low-frequency denoising of synthetic and measured room impulse responses compared to the baseline method, leading to more accurate estimation of acoustic parameters such as decay time.

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.

Desk Editor's Note private letter to a colleague

The paper adds dictionary learning on wavelet approximation coefficients with decay-envelope tolerance to denoise low frequencies in room impulse responses, but the abstract supplies no metrics to back the improvement claim.

read the letter

The paper's main advance is a post-processing step for wavelet-based room impulse response denoising. It uses sparse dictionary learning on the approximation coefficients and sets a time-varying tolerance based on an exponential decay envelope to handle low frequencies better than standard thresholding alone. This targets a known weakness where detail-coefficient methods leave low-frequency content noisy or untouched. The integration of dictionary learning with the decay model for adaptive tolerance is the specific extension that goes beyond prior wavelet work on RIRs. It makes sense for this domain because impulse responses have a structured energy decay that can inform how strictly to reconstruct each time segment. The approach is a reasonable engineering move that could help downstream tasks like estimating decay times or other acoustic parameters. The experiments are described as covering both synthetic and measured data, which is the right mix for this kind of applied work. On the soft spots, the abstract asserts significant gains in low-frequency denoising and parameter accuracy but includes no numbers, error bars, or statistical comparisons. That leaves the central claim unsupported in the visible summary. The decay-envelope adaptation also carries a risk of circularity or bias if its parameters are derived from the same RIR being processed, especially when real responses include modal ringing or non-exponential early parts. The stress-test concern about tolerance mismatch distorting T60 estimates looks worth checking directly in the results. This is aimed at audio signal processing and room acoustics researchers who routinely clean measured impulse responses. Readers who need incremental tools for full-band denoising would get practical value if the full experiments and controls are solid. It deserves a serious referee because the problem is real and the method is focused, even though the evidence needs more detail and scrutiny. I recommend sending it to peer review.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes a wavelet-domain post-processing algorithm for full-band denoising of room impulse responses (RIRs). After standard thresholding of detail coefficients, it applies sparse dictionary learning to the approximation coefficients using a time-varying reconstruction error tolerance. This tolerance is adapted according to local signal-to-noise ratio via an exponential decay envelope model. The authors claim that the method yields significant improvements in low-frequency denoising for both synthetic and measured RIRs relative to the baseline, resulting in more accurate estimation of acoustic parameters such as decay time.

Significance. If the quantitative improvements and lack of bias in decay estimation can be demonstrated, the work would address a recognized limitation of detail-coefficient thresholding at low frequencies and could be useful for acoustic simulation and parameter extraction. The combination of dictionary learning with an SNR-adaptive tolerance schedule is a reasonable extension of existing wavelet techniques. No machine-checked proofs, reproducible code, or parameter-free derivations are reported.

major comments (2)

Abstract: the central claim of 'significant improvement' in low-frequency denoising and 'more accurate estimation of acoustic parameters such as decay time' is unsupported by any quantitative metrics, error bars, statistical tests, or details on validation of the dictionary learning step and tolerance adaptation; this absence is load-bearing because the abstract is the sole location where results are summarized.
Method section describing the time-varying error tolerance: the exponential decay envelope used to set reconstruction accuracy for approximation coefficients risks circularity, because its parameters (decay rate and initial amplitude) appear to be derived from the same RIR being denoised; when the actual RIR deviates from the ideal model (e.g., due to low-frequency modal ringing or non-diffuse reflections), the tolerance schedule can systematically bias the reconstructed decay envelope and subsequent T60 estimates.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address the major comments below and have made revisions to strengthen the presentation of our results and clarify the methodological details.

read point-by-point responses

Referee: [—] Abstract: the central claim of 'significant improvement' in low-frequency denoising and 'more accurate estimation of acoustic parameters such as decay time' is unsupported by any quantitative metrics, error bars, statistical tests, or details on validation of the dictionary learning step and tolerance adaptation; this absence is load-bearing because the abstract is the sole location where results are summarized.

Authors: We agree that the abstract would benefit from quantitative support for the claims. In the revised manuscript, we have updated the abstract to include specific quantitative metrics from our experiments on both synthetic and measured RIRs, such as the reported SNR improvements in low-frequency bands and the reduction in T60 estimation bias and variance. We have also included a brief mention of the cross-validation used for dictionary learning parameters and the tolerance adaptation. This ensures the abstract is self-contained while summarizing the key findings with supporting evidence. revision: yes
Referee: [—] Method section describing the time-varying error tolerance: the exponential decay envelope used to set reconstruction accuracy for approximation coefficients risks circularity, because its parameters (decay rate and initial amplitude) appear to be derived from the same RIR being denoised; when the actual RIR deviates from the ideal model (e.g., due to low-frequency modal ringing or non-diffuse reflections), the tolerance schedule can systematically bias the reconstructed decay envelope and subsequent T60 estimates.

Authors: We thank the referee for highlighting this potential issue. Upon review, the parameters of the exponential decay envelope are estimated from the early portion of the noisy RIR, where the direct sound and early reflections dominate and SNR is high, using a robust least-squares fit that is not affected by the later noisy tail. This estimation is performed prior to the dictionary learning step on the approximation coefficients, avoiding direct circularity with the denoised output. We have clarified this procedure in the revised method section. Furthermore, we have added a new subsection discussing the model assumptions and included results from a sensitivity analysis demonstrating that the method does not introduce significant bias in T60 estimates even for RIRs with modal ringing. revision: partial

Circularity Check

0 steps flagged

No significant circularity; modeling choice is independent of target result

full rationale

The provided abstract and context describe a wavelet denoising extension that applies sparse dictionary learning to approximation coefficients, with reconstruction tolerance adapted via an exponential decay envelope to match local SNR. This envelope is a standard acoustic prior for RIR energy decay and is not shown to be fitted in a way that forces the denoised output's decay parameters to match the input by construction. No equations, self-citations, or uniqueness claims are present that reduce the claimed improvement in low-frequency denoising or T60 estimation to a tautology. The method's output is presented as an empirical result on synthetic and measured data rather than a definitional identity. No load-bearing steps match the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The approach rests on standard wavelet properties and the domain assumption that RIRs follow exponential decay; no new entities are postulated.

free parameters (2)

dictionary size and sparsity level
Parameters of the sparse dictionary learning step that must be chosen or tuned.
exponential decay rate and initial amplitude
Parameters of the envelope model used to set time-varying tolerance.

axioms (2)

standard math Discrete wavelet transform separates approximation and detail coefficients with perfect reconstruction
Invoked when applying denoising only to approximation coefficients while preserving the transform structure.
domain assumption Room impulse responses exhibit approximately exponential energy decay
Used to construct the local SNR model that controls reconstruction tolerance.

pith-pipeline@v0.9.0 · 5404 in / 1312 out tokens · 55285 ms · 2026-05-07T10:37:07.426125+00:00 · methodology

discussion (0)

Reference graph

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It inherently captures the acoustic properties of the source, the receiver, and the environment

INTRODUCTION The room impulse response (RIR) characterizes the transfer function between a sound source and a receiver in a room. It inherently captures the acoustic properties of the source, the receiver, and the environment. RIRs are widely used in ap- plications ranging from auralization and immersive technolo- gies such as virtual and augmented realit...
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Full band denoising of room impulse response in the wavelet domain with dictionary learning

MODEL The proposed denoising algorithm builds on the wavelet- domain approach introduced by [9]. The diagram in Figure 1 outlines the workflow of the proposed denoising algo- rithm. It begins with the discrete wavelet transform (Section 2.1), which decomposes the RIR into approximation and de- tail coefficients. The detail coefficients are denoised using ...

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For this purpose, both methods are compared on a set of numerical experiments where low-frequency noise have been artificially added

RESULTS Numerical experiments were conducted on both simulated and experimental data, with the primary objective of enhanc- ing the low-frequency denoising performance of the baseline method [9]. For this purpose, both methods are compared on a set of numerical experiments where low-frequency noise have been artificially added. For these experiments, the ...
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The proposed approach outperforms the baseline, yielding more accurate RIR mea- surements and improved estimation of acoustic parameters especially in low frequencies

CONCLUSION This work introduced a wavelet-based post-processing method that extends denoising to low frequencies through sparse DL with adaptive error control. The proposed approach outperforms the baseline, yielding more accurate RIR mea- surements and improved estimation of acoustic parameters especially in low frequencies. Further works would be to in-...
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