Dual-Domain Enhancement Module (DDE)

• Dual-Domain Enhancement Module (DDE) is a design principle that jointly processes paired domains—such as spatial and frequency—to preserve fine details and structural fidelity.
• Architectural patterns in DDE follow a decomposition-enhancement-reconstruction approach using methods like DWT, Fourier transforms, and gradient extraction.
• Empirical results across tasks such as low-light enhancement and multimodal fusion show significant improvements in PSNR, SSIM, and detection metrics with DDE implementations.

Searching arXiv for papers using or closely related to “Dual-Domain Enhancement Module (DDE)” across imaging and signal-processing contexts. Dual-Domain Enhancement Module (DDE) denotes a class of architectures that enhance a signal by jointly modeling two complementary representational domains rather than relying on a single feature space. In the cited literature, the paired domains are most often spatial and frequency/Fourier, but the same design principle also appears as color-gradient decomposition for low-light enhancement, spatial-spectral learning for underwater restoration, frequency-delay expansion for CSI prediction, and RGB–optical-flow differential fusion for video saliency. The term is used most explicitly in DEPF, where DDE combines Cross-Scale Wavelet Mamba (CSWM) and Fourier Details Recovery (FDR) to brighten low-light RGB remote-sensing images and recover texture details before multimodal fusion (Li et al., 9 Sep 2025). Closely related dual-domain modules appear in multimodal CT-PET synthesis (Steele et al., 11 Jun 2026), low-light enhancement (Qu et al., 2023, Yao et al., 2024), underwater image enhancement (Peng et al., 27 Apr 2025, Pokuri et al., 17 Apr 2026), infrared-visible fusion (Zhang et al., 5 Sep 2025), UAV detection (Zhang et al., 3 Apr 2026), and other signal-processing settings.

1. Conceptual scope and defining characteristics

The cited literature does not present DDE as a single canonical block. Instead, it presents a recurring architectural idea: decompose the input into two domains with complementary inductive biases, perform domain-specific enhancement, and then reconcile the enhanced representations for reconstruction, fusion, synthesis, or prediction. In DEPF, the two domains are low-frequency wavelet content and Fourier spectra; in DDE-GAN, they are image and frequency/measurement domains; in SS-UIE, they are spatial and spectral branches; and in DDNet, they are color and gradient domains rather than spatial and Fourier domains (Li et al., 9 Sep 2025, Steele et al., 11 Jun 2026, Peng et al., 27 Apr 2025, Qu et al., 2023).

This literature suggests that DDE is better understood as a methodological family than as a fixed module specification. The family resemblance lies in coordinated enhancement across paired representations. One domain typically carries global illumination, structure, or low-frequency content, while the other carries edges, gradients, phase, high-frequency detail, or measurement-domain constraints. The dual-domain formulation is therefore used when single-domain processing is described as insufficient for preserving fine details, maintaining structural fidelity, handling degradation heterogeneity, or modeling long-range dependencies (Yao et al., 2024, Pokuri et al., 17 Apr 2026, Zhang et al., 5 Sep 2025, Zhang et al., 3 Apr 2026).

2. Architectural patterns

A common structural pattern is decomposition-enhancement-reconstruction. DEPF first applies N-level Haar 2D-DWT, enhances the low-frequency component through CSWM, reconstructs through inverse DWT, and then applies FDR in the Fourier domain (Li et al., 9 Sep 2025). DDNet divides enhancement into color enhancement and gradient enhancement through CEM and LoG-based GEM inside an encoder-decoder, followed by a final fusion decoder (Qu et al., 2023). DFFN formalizes enhancement as two sequential phases—amplitude illumination and phase refinement—with information exchange through IFAM (Yao et al., 2024). DDE-GAN uses paired generators in image and frequency domains and trains them through hierarchical dual-domain constraints (Steele et al., 11 Jun 2026).

Work	Paired domains	Stated components
DEPF (Li et al., 9 Sep 2025)	Wavelet low-frequency / Fourier spectrum	CSWM, FDR
DDNet (Qu et al., 2023)	Color / gradient	CEM, GEM
DFFN (Yao et al., 2024)	Amplitude / phase	DDAB, DDPB, IFAM
DDE-GAN (Steele et al., 11 Jun 2026)	Image / frequency or measurement	Dual generators, forward and inverse transforms
SS-UIE (Peng et al., 27 Apr 2025)	Spatial / spectral	MCSS, SWSA, SS-block
SFFNet (Zhang et al., 3 Apr 2026)	Spatial edges / frequency edges	MDDC, DEIE

Parallelism and hierarchy are both recurrent. SS-UIE splits features into two halves, sends one through SWSA and the other through MCSS, concatenates the outputs, and adds a residual connection (Peng et al., 27 Apr 2025). Hero-Mamba processes the RGB image and FFT-derived spectral components in parallel and concatenates the outputs of Mamba-based SS2D blocks (Pokuri et al., 17 Apr 2026). By contrast, DFFN is explicitly stage-wise: amplitude is learned first to restore brightness, and phase is learned second to refine details (Yao et al., 2024). The choice between parallel and stage-wise organization reflects the specific role assigned to each domain: simultaneous complementarity in some settings, ordered correction in others.

3. Domain decompositions and operators

The operators used in DDE implementations vary substantially, but they all create a controlled separation of information types. In DEPF, wavelet decomposition is written as

$$LL, [HL, LH, HH]_n, \ldots, [HL, LH, HH]_1 = DWT(I_v),$$

after which CSWM enhances the low-frequency component via

$LL_e = LL \times \sum_i SSM(f_{seq}^i),$

and FDR derives amplitude and phase through FFT, enhances them with spectrum recovery networks, and reconstructs the output as

$I_{VE} = IFFT(AS_e, PS_e).$

This formulation makes the low-frequency branch responsible for global brightness and the Fourier branch responsible for texture-detail recovery (Li et al., 9 Sep 2025).

DFFN uses Fourier amplitude and phase as explicit task variables rather than as auxiliary features. Its first-stage supervision target is

$$\text{Target}_1 = \mathcal{F}^{-1}\left(\mathcal{A}(I_{gt}), \mathcal{P}(I_{low})\right),$$

and the second stage receives

$$I_{mix} = \mathcal{F}^{-1}\left(\mathcal{A}(O_A), \mathcal{P}(I_{low})\right).$$

The resulting decomposition assigns brightness restoration to amplitude and detail refinement to phase (Yao et al., 2024).

Other DDE variants replace Fourier amplitude-phase analysis with alternative pairings. DDNet computes a LoG-based gradient map, concatenates it with the low-light image, and uses gradient-domain supervision for GEM alongside color-domain supervision for CEM (Qu et al., 2023). SFFNet performs frequency-domain high-pass filtering, retains only frequencies above a threshold $\alpha$, and modulates frequency magnitudes with a spatial edge-strength term $S(i,j)$ before inverse transformation (Zhang et al., 3 Apr 2026). ChannelKAN generates a delay-domain CSI branch by applying IDFT to the frequency-domain CSI, then fuses the two streams downstream (Jiang et al., 11 May 2026). In each case, dual-domain enhancement depends not on a particular transform, but on an explicit partition between complementary signal attributes.

4. Optimization and supervision

DDE methods usually enforce consistency in both domains during training rather than relying solely on a final reconstruction loss. DDNet uses a joint loss composed of $\mathcal{L}_{Lap}$, $\mathcal{L}_{Coarse}$, and $\mathcal{L}_{Final}$, with typical weights $LL_e = LL \times \sum_i SSM(f_{seq}^i),$0, $LL_e = LL \times \sum_i SSM(f_{seq}^i),$1, and $LL_e = LL \times \sum_i SSM(f_{seq}^i),$2. The first two terms are $LL_e = LL \times \sum_i SSM(f_{seq}^i),$3 losses for gradient and color supervision, and the final term is SSIM-based supervision for the fused output (Qu et al., 2023).

DDE-GAN organizes optimization into three stages. Stage 1 enforces intra-domain consistency in image and frequency domains. Stage 2 adds inter-domain consistency through forward and inverse projection operators. Stage 3 introduces rotational equivariance, expressed in the paper through constraints of the form

$LL_e = LL \times \sum_i SSM(f_{seq}^i),$4

This loss design makes the dual-domain formulation physically informed rather than merely feature-complementary (Steele et al., 11 Jun 2026).

Several works add domain-aware regularization terms that directly emphasize difficult frequencies or degraded subbands. SS-UIE introduces Frequency-Wise Loss (FWL) and combines it with pixel-domain supervision as

$LL_e = LL \times \sum_i SSM(f_{seq}^i),$5

where the frequency loss dynamically upweights harder frequency components (Peng et al., 27 Apr 2025). GD$LL_e = LL \times \sum_i SSM(f_{seq}^i),$6Fusion uses intensity, texture, and color losses,

$LL_e = LL \times \sum_i SSM(f_{seq}^i),$7

with $LL_e = LL \times \sum_i SSM(f_{seq}^i),$8, $LL_e = LL \times \sum_i SSM(f_{seq}^i),$9, and $I_{VE} = IFFT(AS_e, PS_e).$0, thereby coupling degradation suppression and fusion in an end-to-end objective rather than a decoupled pre-enhancement pipeline (Zhang et al., 5 Sep 2025). A plausible implication is that dual-domain enhancement is most effective when the training objective preserves the decomposition logic imposed by the architecture.

5. Applications and empirical record

DDE-style modules have been reported in enhancement, synthesis, fusion, detection, and prediction tasks.

Work	Task	Reported result
DDNet (Qu et al., 2023)	UHD low-light enhancement	4K $I_{VE} = IFFT(AS_e, PS_e).$1 at over 35 FPS; LOL PSNR 21.86, SSIM 0.832, NIQE 3.38
DDE-GAN (Steele et al., 11 Jun 2026)	CT-PET synthesis	SSIM $I_{VE} = IFFT(AS_e, PS_e).$2; PSNR $I_{VE} = IFFT(AS_e, PS_e).$3
Hero-Mamba (Pokuri et al., 17 Apr 2026)	Underwater enhancement on LSUI	PSNR 25.802; SSIM 0.913
SFFNet-X (Zhang et al., 3 Apr 2026)	UAV detection	36.8 AP on VisDrone; 20.6 AP on UAVDT
ChannelKAN (Jiang et al., 11 May 2026)	CSI prediction	NMSE 0.0265; SE 6.414; BER 0.00771

The empirical pattern is not restricted to image quality metrics. DDNet reports that object detection and scene segmentation improve on enhanced images in low-light ITS settings, and it is explicitly designed for real-time UHD surveillance (Qu et al., 2023). DDE-GAN reports superior multimodal synthesis quality on the HECKTOR 2022 CT-PET dataset and attributes part of the gain to joint dual-domain learning with geometric equivariance (Steele et al., 11 Jun 2026). In underwater enhancement, Hero-Mamba attributes its gains to parallel processing of spatial RGB and FFT components, while SS-UIE attributes its gains to adaptive spatial-spectral modeling with linear complexity (Pokuri et al., 17 Apr 2026, Peng et al., 27 Apr 2025). In aerial detection, SFFNet reports that dual-domain edge enhancement improves AP over single-domain variants, while DEPF reports significant performance gains when CSWM and FDR are used together before multispectral fusion (Zhang et al., 3 Apr 2026, Li et al., 9 Sep 2025). ChannelKAN’s ablation study further reports degradation from NMSE 0.0265 to 0.0318, from SE 6.414 to 6.385, and from BER 0.00771 to 0.00799 when dual-domain processing is removed (Jiang et al., 11 May 2026).

6. Variants, misconceptions, and terminological boundaries

A common misconception is that DDE always denotes spatial-frequency image enhancement. The cited literature shows otherwise. DDNet defines the two domains as color and gradient (Qu et al., 2023). The video salient object detection framework with Confidence-guided Adaptive Gate and Dual Differential Enhancement defines them as RGB and optical flow streams and enhances each stream by modeling feature differences,

$I_{VE} = IFFT(AS_e, PS_e).$4

before concatenation and fusion (Chen et al., 2021). ChannelKAN uses frequency and delay domains rather than pixel and spectrum (Jiang et al., 11 May 2026).

A second misconception is that DDE must be a standalone preprocessor. In practice, it may appear before a detector, inside a GAN, within a feature pyramid, or as part of a joint fusion pipeline. DEPF places DDE before RGB backbone extraction (Li et al., 9 Sep 2025). DDE-GAN embeds dual-domain learning inside both generator and discriminator losses (Steele et al., 11 Jun 2026). GD$I_{VE} = IFFT(AS_e, PS_e).$5Fusion distributes dual-domain processing across GFMSE and GSMAF branches and trains them jointly with the fusion network (Zhang et al., 5 Sep 2025). SFFNet integrates dual-domain edge enhancement into MDDC inside the detector backbone and neck (Zhang et al., 3 Apr 2026).

The acronym itself is overloaded. In generative modeling, DDE can also mean Diffusion Domain Expansion, a method that coordinates multiple runs of a pre-trained diffusion model through a compact coordinator network; this usage is unrelated to dual-domain enhancement (Lifar et al., 22 May 2026). Comparable dual-domain logic also appears without the exact DDE label in MDPhD for time- and frequency-domain speech enhancement, D2Former for fully complex time-frequency speech enhancement, D$I_{VE} = IFFT(AS_e, PS_e).$6Fusion for spatial-frequency deepfake detection, and DDSRNet for spatial-wavelet hyperspectral super-resolution (Kim et al., 2018, Zhao et al., 2023, Qiu et al., 21 Mar 2025, Karayaka et al., 10 Dec 2025). This suggests that, in contemporary arXiv usage, “Dual-Domain Enhancement Module” functions less as a uniquely standardized module name than as a broadly reusable design principle for coupling complementary representational domains under task-specific supervision.