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arxiv: 1907.03128 · v1 · pith:YOHXSMQ4new · submitted 2019-07-06 · 💻 cs.CV · eess.IV

Multi-level Wavelet Convolutional Neural Networks

Pengju Liu , Hongzhi Zhang , Wei Lian , Wangmeng Zuo This is my paper

Pith reviewed 2026-05-25 01:33 UTC · model grok-4.3

classification 💻 cs.CV eess.IV
keywords wavelet transformconvolutional neural networkimage restorationreceptive fieldU-Netdenoisingsuper-resolutionpooling
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The pith

Multi-level wavelet transforms embedded in CNNs allow larger receptive fields with less information loss than pooling or dilated convolutions.

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

The paper introduces a multi-level wavelet CNN that inserts wavelet decomposition into the network to downsample features while expanding the receptive field. This is intended to overcome the information loss from pooling and the gridding artifacts from dilated filters. The architecture uses a U-Net base with inverse wavelet transforms to rebuild high-resolution maps for image restoration tasks. A sympathetic reader would care because it promises a more efficient way to handle large context in convolutional networks for vision problems. The model is also positioned as a generalization of average pooling applicable to classification.

Core claim

By embedding the wavelet transform into the CNN, the MWCNN reduces the resolution of feature maps to increase the receptive field size while preserving information better than pooling, and uses inverse wavelet transform to reconstruct the high resolution feature maps from the decomposed versions. This provides a better trade-off between receptive field and computational efficiency, and can replace pooling operations in CNNs.

What carries the argument

The multi-level wavelet transform (with inverse) embedded at multiple levels in the U-Net architecture to decompose and reconstruct feature maps.

If this is right

  • Improved results on image denoising, single image super-resolution, and JPEG artifact removal compared to prior methods.
  • Effective replacement for pooling in any CNN that requires downsampling operations.
  • Generalization of average pooling and improvement over dilated filters without checkerboard patterns.
  • Extension to object classification tasks with maintained efficiency.

Where Pith is reading between the lines

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

  • Wavelet-based downsampling might preserve frequency information better in other signal processing tasks beyond images.
  • If the reconstruction is artifact-free, similar embeddings could be tested in video or 3D CNNs for temporal or volumetric data.
  • The approach could lead to parameter-free ways to control receptive field growth in network design.

Load-bearing premise

The inverse wavelet transform can reconstruct high-resolution feature maps from the low-resolution wavelet coefficients without adding significant artifacts or losing the efficiency advantage.

What would settle it

A direct comparison experiment where MWCNN is applied to a standard benchmark like BSD68 for denoising and shows no improvement in PSNR or SSIM over a baseline U-Net with strided convolutions or pooling at equivalent computational cost.

Figures

Figures reproduced from arXiv: 1907.03128 by Hongzhi Zhang, Pengju Liu, Wangmeng Zuo, Wei Lian.

Figure 1
Figure 1. Figure 1: The running time vs. PSNR value of representative [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: From WPT to MWCNN. Intuitively, WPT can be seen [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Multi-level wavelet-CNN architecture. It consists of two parts: the contracting and expanding subnetworks. Each solid [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of average pooling, dilated filter and the proposed MWCNN. Take one CNN block as an example: (a) sum-pooling with factor 2 leads to the most significant information loss which is not suitable for image restoration; (b) dilated filtering with rate 2 is equal to shared parameter convolution on sub-images; (c) the proposed MWCNN first decomposes an image into 4 sub-bands and then concatenates the… view at source ↗
Figure 5
Figure 5. Figure 5: Illustration of the gridding effect. Taken 3-layer CNNs as an example: (a) the dilated filtering with rate 2 suffers from large amount of information loss, (b) the two neighbored pixels are based on information from totally non-overlapped locations, and (c) our MWCNN can perfectly avoid underlying drawbacks. Compared with dilated filtering, MWCNN can also avoid the gridding effect. With the increase of dep… view at source ↗
Figure 6
Figure 6. Figure 6: Image denoising results of “T est044” (Set68) with noise level of 50. TABLE II: Average PSNR(dB) / SSIM results of the competing methods for SISR with scale factors S = 2, 3 and 4 on datasets Set5, Set14, BSD100 and Urban100. Red color indicates the best performance. Dataset S VDSR [2] DnCNN [5] RED30 [20] SRResNet [11] LapSRN [3] DRRN [17] MemNet [19] WaveResNet [45] SRMDNF [44] MWCNN(P) MWCNN Set5 ×2 37.… view at source ↗
Figure 7
Figure 7. Figure 7: Single image super-resolution: result of “253027” (BSD100) with upscaling factor of ×4. network. For qualitative comparisons, we use source codes of nine CNN-based methods, including VDSR [2], DnCNN [5], RED30 [20], SRResNet [11], LapSRN [3], DRRN [17], Mem￾Net [19], WaveResNet [45] and SRMDNF [44]. Since the source code of SRResNet is not released, their results as shown in Table II are incomplete. And th… view at source ↗
Figure 8
Figure 8. Figure 8: JPEG image artifacts removal: visual results of “carnivaldolls” (LIVE1) with quality factor of 10. the JPEG encoder. In our experiments, MWCNN is compared to four competing methods, i.e., ARCNN [35], TNRD [26], DnCNN [5], and MemNet [19]. The results of MemNet [19] and TNRD [26] are incomplete according to their paper and released source codes. Table III shows the average PSNR/SSIM results of the competing… view at source ↗
read the original abstract

In computer vision, convolutional networks (CNNs) often adopts pooling to enlarge receptive field which has the advantage of low computational complexity. However, pooling can cause information loss and thus is detrimental to further operations such as features extraction and analysis. Recently, dilated filter has been proposed to trade off between receptive field size and efficiency. But the accompanying gridding effect can cause a sparse sampling of input images with checkerboard patterns. To address this problem, in this paper, we propose a novel multi-level wavelet CNN (MWCNN) model to achieve better trade-off between receptive field size and computational efficiency. The core idea is to embed wavelet transform into CNN architecture to reduce the resolution of feature maps while at the same time, increasing receptive field. Specifically, MWCNN for image restoration is based on U-Net architecture, and inverse wavelet transform (IWT) is deployed to reconstruct the high resolution (HR) feature maps. The proposed MWCNN can also be viewed as an improvement of dilated filter and a generalization of average pooling, and can be applied to not only image restoration tasks, but also any CNNs requiring a pooling operation. The experimental results demonstrate effectiveness of the proposed MWCNN for tasks such as image denoising, single image super-resolution, JPEG image artifacts removal and object classification.

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

2 major / 1 minor

Summary. The paper proposes a novel multi-level wavelet CNN (MWCNN) model that embeds the wavelet transform into CNN architectures to achieve a better trade-off between receptive field size and computational efficiency. It uses discrete wavelet transform (DWT) to reduce the resolution of feature maps and inverse wavelet transform (IWT) to reconstruct high-resolution feature maps within a U-Net architecture for image restoration tasks. The model is presented as an improvement over dilated filters and a generalization of average pooling, with claimed applicability to various CNNs and experimental effectiveness on image denoising, single image super-resolution, JPEG artifact removal, and object classification.

Significance. If the results hold, this approach could offer an efficient alternative to pooling and dilated convolutions in CNN design by leveraging wavelet properties for resolution reduction and receptive field expansion without gridding effects or information loss. The conceptual framing as a generalization of pooling is a positive aspect.

major comments (2)
  1. [Abstract] The central claim of experimental effectiveness on four tasks rests on an assertion without any accompanying metrics, baselines, ablation details, or error analysis, which is load-bearing since the soundness of the proposal depends on demonstrated performance gains.
  2. [Abstract] The description of deploying IWT to reconstruct HR feature maps provides no implementation specifics such as the wavelet family, boundary handling, or how differentiability is ensured for backpropagation, leaving the assumption of artifact-free integration unverified for CNN feature maps.
minor comments (1)
  1. [Abstract] The statement that MWCNN 'can be applied to not only image restoration tasks, but also any CNNs requiring a pooling operation' would benefit from more precise examples of such CNNs or operations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below, noting that the abstract serves as a concise summary while the full manuscript provides supporting details and experiments.

read point-by-point responses

  1. Referee: [Abstract] The central claim of experimental effectiveness on four tasks rests on an assertion without any accompanying metrics, baselines, ablation details, or error analysis, which is load-bearing since the soundness of the proposal depends on demonstrated performance gains.

    Authors: The abstract provides a high-level overview of the contributions. Quantitative metrics (e.g., PSNR/SSIM gains), baselines (DnCNN, VDSR, etc.), ablation studies on wavelet decomposition levels, and error analyses are presented in detail in Sections 4.1–4.4 of the manuscript for all four tasks. We can partially revise the abstract to include one or two representative performance numbers if space allows, to better highlight the gains without altering its summary nature. revision: partial

  2. Referee: [Abstract] The description of deploying IWT to reconstruct HR feature maps provides no implementation specifics such as the wavelet family, boundary handling, or how differentiability is ensured for backpropagation, leaving the assumption of artifact-free integration unverified for CNN feature maps.

    Authors: The abstract is intentionally brief. Full implementation details appear in Section 3: we employ the Haar wavelet (orthogonal with perfect reconstruction), use symmetric extension for boundary handling, and note that DWT/IWT are fixed linear operations and thus differentiable, enabling seamless end-to-end backpropagation. Experiments in Section 4 confirm artifact-free integration through visual and quantitative results. No change to the abstract is needed, as these specifics belong in the methods section. revision: no

Circularity Check

0 steps flagged

No circularity: architectural proposal without load-bearing derivations

full rationale

The paper proposes an MWCNN architecture that embeds discrete wavelet transform (DWT) and inverse wavelet transform (IWT) into a U-Net backbone for image restoration tasks. No equations, predictions, or first-principles derivations are presented that reduce to fitted parameters, self-definitions, or self-citation chains. The core claim is an engineering suggestion (wavelet-based downsampling as an alternative to pooling or dilation), supported by experimental results on standard tasks rather than any mathematical equivalence to its inputs. Self-citations, if present in the full text, are not load-bearing for the central architectural idea. This is a standard non-circular model proposal.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated premise that wavelet transforms integrate cleanly into CNN feature maps.

pith-pipeline@v0.9.0 · 5757 in / 1094 out tokens · 21455 ms · 2026-05-25T01:33:29.653982+00:00 · methodology

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Reference graph

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