Frequency Illumination Adaptor (FIA)

• Frequency Illumination Adaptor (FIA) is a specialized Fourier-based illumination correction branch within RetinexDual that targets global color, exposure, and illumination distortions.
• FIA employs lightweight Fourier Correction Blocks to process amplitude and phase of illumination feature maps, yielding improved PSNR and SSIM with minimal parameter overhead.
• By isolating global illumination from localized structural details, FIA enables targeted spectral enhancements essential for UHD tasks like low-light enhancement and dehazing.

Searching arXiv for "Frequency Illumination Adaptor" and closely related work to ground the article in current literature. The Frequency Illumination Adaptor (FIA) is the illumination-correction sub-network in "RetinexDual" (Kishawy et al., 6 Aug 2025), a Retinex theory-based framework for generalized ultra-high-definition image restoration. Within that framework, FIA operates on the illumination component rather than the full RGB image, and it is designed to correct color and illumination distortions in the frequency domain while a separate branch, SAMBA, restores structural degradations in the spatial domain. FIA is therefore not a general-purpose spectral restoration block, but a specialized adaptor for the Retinex illumination term $L_{\text{eff}}$, where global context, low-frequency regularity, and color-dominated spectral structure are most useful (Kishawy et al., 6 Aug 2025).

1. Retinex formulation and the formal role of FIA

RetinexDual is built on the decomposition

$I = R \odot L,$

where $R\in\mathbb{R}^{H\times W\times 3}$ denotes reflectance and $L\in\mathbb{R}^{H\times W}$ denotes illumination. For distorted inputs, the model adopts a Retinex-extended degradation view in which structural corruption and illumination corruption are treated separately. A Retinex decomposer $\psi_d$ predicts corrupted components directly from the distorted input $x$, producing $R_{\text{eff}}$ and $L_{\text{eff}}$. The restoration branches then estimate corrections for these components through

$$R = R_{\text{eff}} + \mathcal{S}(R_{\text{eff}}),\qquad L = L_{\text{eff}} + \mathcal{F}(L_{\text{eff}}),$$

followed by recomposition

$I = R \odot L.$

Here $I = R \odot L,$0 is SAMBA and $I = R \odot L,$1 is FIA (Kishawy et al., 6 Aug 2025).

Within this decomposition, FIA is explicitly the illumination branch. Its responsibility is not blur removal, rain-streak suppression, or detail reconstruction; those are assigned to SAMBA. FIA instead targets $I = R \odot L,$2, the corruption associated with color, exposure, and illumination. The design therefore assumes that illumination-related degradation is more global and more amenable to frequency-domain treatment than the spatially confined artifacts that dominate the reflectance side.

This branch separation is the central meaning of the "dual nature" formulation. RetinexDual does not apply a single generic architecture to both components. It uses a spatial, multi-scale, Mamba-based encoder-decoder for reflectance and a lightweight Fourier-based module for illumination. A plausible implication is that FIA should be understood less as a stand-alone restoration backbone than as a domain-specialized adaptor whose validity depends on Retinex disentanglement.

2. Motivation: degradation locality and illumination as a frequency-domain target

The motivation for FIA follows from two observations in RetinexDual. First, extreme downsampling followed by restoration and upsampling loses UHD detail because resampling is decoupled from enhancement. Second, pure frequency-domain UHD image restoration suffers from a degradation locality problem: localized blur, raindrops, and similar artifacts are not well represented when the image is treated only through global spectral filtering (Kishawy et al., 6 Aug 2025).

The paper supports this with a frequency analysis. For a dehazing case, the PSNR between degraded and ground truth is reported as 14.17 dB in the spatial domain and 21.44 dB in the frequency domain. For a deblurring case, the spatial-domain PSNR is 24.69 dB, whereas the frequency-domain PSNR is 18.15 dB. The interpretation given is that global haze is more regular in frequency space, while localized blur is better captured in the spatial domain.

From this analysis, FIA is restricted to the illumination component $I = R \odot L,$3. The rationale is that illumination distortion is largely global, including exposure shifts and color tint, and that frequency-domain global context is therefore beneficial. By contrast, structural degradations remain in the reflectance branch, where locality is preserved. The authors summarize the underlying claim as follows: pure frequency-domain approaches are ineffective for spatially confined image artifacts, primarily due to the loss of degradation locality (Kishawy et al., 6 Aug 2025).

This design also rests on a spectral interpretation of illumination corruption. The paper states that illumination distortion manifests as low-frequency patterns and color-dominated amplitude patterns. FIA uses this by operating in the Fourier domain, separating amplitude and phase, adjusting them with learned $I = R \odot L,$4 convolutions, and reconstructing via IFFT. This suggests that FIA is not merely "using FFT" but specifically exploiting the asymmetry between global illumination/color statistics and local structural corruption.

3. Architecture: FIA as a stack of Fourier Correction Blocks

FIA processes illumination feature maps rather than the full RGB image. At a given scale, its input is described generically as

$I = R \odot L,$5

Its internal operation is entirely frequency-centric, using FFT and IFFT, but its inputs and outputs are spatial feature maps. In the full RetinexDual pipeline, FIA is applied to $I = R \odot L,$6 at each output level, and the restored image at each scale is produced by Retinex recomposition $I = R \odot L,$7 with deep supervision on three scales $I = R \odot L,$8 (Kishawy et al., 6 Aug 2025).

The explicit building block of FIA is the Fourier Correction Block (FCB). FCB is described as compact, fully frequency-aware, and stabilized through multiplicative fusion and residual scaling. It contains roughly 0.2M parameters, making it a small component relative to the overall 4.726M-parameter RetinexDual model.

Given input $I = R \odot L,$9, FCB first applies layer normalization and FFT: $R\in\mathbb{R}^{H\times W\times 3}$0 The resulting spectrum is then decomposed into amplitude $R\in\mathbb{R}^{H\times W\times 3}$1 and phase $R\in\mathbb{R}^{H\times W\times 3}$2. Each component is processed by two $R\in\mathbb{R}^{H\times W\times 3}$3 convolutions separated by a ReLU. The paper also provides a compact formulation: $R\in\mathbb{R}^{H\times W\times 3}$4 where Conv denotes $R\in\mathbb{R}^{H\times W\times 3}$5 convolutions on the frequency representation. After inverse transformation, the reconstructed signal $R\in\mathbb{R}^{H\times W\times 3}$6 modulates the original input multiplicatively,

$R\in\mathbb{R}^{H\times W\times 3}$7

and a final spatial refinement with residual scaling is applied: $R\in\mathbb{R}^{H\times W\times 3}$8 Here Conv3 is a $R\in\mathbb{R}^{H\times W\times 3}$9 convolution and $L\in\mathbb{R}^{H\times W}$0 is a learnable residual scale (Kishawy et al., 6 Aug 2025).

The intended effect is illumination adaptation rather than geometric correction. The amplitude spectrum is associated with color and lighting magnitude, while phase is associated with geometry and detail. FCB therefore learns frequency-aware adjustments that reweight spectral components and re-express those adjustments as a spatially varying gain after IFFT. The multiplicative term $L\in\mathbb{R}^{H\times W}$1 is described as akin to adaptive illumination adjustment. The final $L\in\mathbb{R}^{H\times W}$2 convolution smooths and refines the adjusted illumination feature.

4. Interaction with SAMBA and the Retinex recomposition mechanism

FIA and SAMBA interact only through decomposition and recomposition. There is no cross-attention or feature concatenation between branches. The pipeline is

1. $L\in\mathbb{R}^{H\times W}$3 via the decomposer,
2. $L\in\mathbb{R}^{H\times W}$4 via SAMBA,
3. $L\in\mathbb{R}^{H\times W}$5 via FIA,
4. $L\in\mathbb{R}^{H\times W}$6 at each scale,
5. supervision of each $L\in\mathbb{R}^{H\times W}$7 against the ground truth at that scale (Kishawy et al., 6 Aug 2025).

This strict separation preserves the intended semantics of each branch. FIA affects only illumination and color, while SAMBA affects structure. The paper characterizes the final multiplication $L\in\mathbb{R}^{H\times W}$8 as physically meaningful reconstruction under the Retinex interpretation. A plausible implication is that FIA should not be read as a generic spectral enhancement module attached arbitrarily to a restoration network; its effect is constrained by the assumption that illumination and reflectance remain disentangled during processing.

Training also reinforces the frequency-aware role of FIA. The total loss combines spatial and frequency terms: $L\in\mathbb{R}^{H\times W}$9 with

$\psi_d$0

Deep supervision across three scales is

$\psi_d$1

The FFT loss is global and encourages frequency-distribution agreement between prediction and ground truth, which directly supports FIA’s illumination-domain spectral adaptation (Kishawy et al., 6 Aug 2025).

The task suite further clarifies branch specialization. RetinexDual is trained and evaluated on Low-Light Enhancement (UHD-LL), Dehazing (UHD-Haze), Deraining (4K-Rain13K), and Deblurring (UHD-Blur). The paper states that FIA is especially critical when global illumination and color issues are prominent, particularly in low-light enhancement and dehazing. At the same time, improvements on deraining and deblurring indicate that a dedicated illumination branch remains useful even when the dominant degradation is structural.

5. Empirical behavior, ablations, and computational suitability for UHD

RetinexDual reports that FIA is necessary both architecturally and quantitatively. In the key-contribution ablation, removing Fourier processing from the illumination branch ("A: w/o Fourier") yields PSNR 27.03, SSIM 0.919, and 4.682M parameters. The full model yields PSNR 28.79, SSIM 0.934, and 4.726M parameters. This corresponds to a gain of +1.76 dB PSNR and +0.015 SSIM for an increase of roughly 0.04M parameters (Kishawy et al., 6 Aug 2025).

A separate ablation removes the illumination branch altogether ("C: w/o FIA branch"), yielding PSNR 26.67 and SSIM 0.919, compared with 28.79 / 0.934 for the full model. In the paper’s interpretation, this confirms that illumination correction is necessary across all four tasks, not only in low-light settings. The evidence is particularly strong because the degradation modeled by FIA is not restricted to one benchmark family.

Complexity claims are similarly specific. FIA is presented as suitable for UHD because FCB is compact, FFT/IFFT have $\psi_d$2 complexity, and the framework avoids extreme downsampling. Table 9 reports 4K-image inference times of 0.957 s for Wave-Mamba, 0.601 s for ERR, 1.63 s for D2Net, and 0.955 s for RetinexDual. The reported comparison therefore places RetinexDual as competitive with Wave-Mamba, faster than D2Net, and slower than ERR. The paper attributes only a modest share of this cost to FIA relative to SAMBA (Kishawy et al., 6 Aug 2025).

Several interpretive points follow from these results. FIA is not the dominant computational burden in RetinexDual, and its contribution is not merely cosmetic color adjustment. The ablations indicate substantive gains in both PSNR and SSIM with very limited parameter growth. At the same time, FIA is not presented as sufficient on its own; its efficacy depends on the complementary spatial restoration performed by SAMBA.

6. Related mechanisms, limitations, and terminological ambiguity

Frequency-based illumination adaptation has related antecedents, but FIA in the strict sense refers to the illumination branch in RetinexDual. A related precursor appears in "Lightweight HDR Camera ISP for Robust Perception in Dynamic Illumination Conditions via Fourier Adversarial Networks" (Shyam et al., 2022). That work proposes a two-stage enhancement pipeline with illumination balancing and restoration, plus a Fourier spectrum-based adversarial framework. Its discriminator operates on grayscale FFT-derived magnitude and phase, and its stated objective is consistent image enhancement under varying illumination conditions. This suggests an earlier line of research in which illumination correction is constrained by spectral structure, although it does not instantiate the RetinexDual formulation or the FCB-based illumination branch.

Another related design appears in "AQUA-Net: Adaptive Frequency Fusion and Illumination Aware Network for Underwater Image Enhancement" (Ali et al., 5 Dec 2025). AQUA-Net combines a frequency branch that modulates Fourier magnitude while keeping phase unchanged and an illumination branch that estimates a bounded illumination map

$\psi_d$3

Its decoder uses illumination-modulated skip connections

$\psi_d$4

This is not the same object as FIA, but it reinforces the broader design pattern that frequency cues and illumination cues can provide complementary corrections when kept architecturally distinct.

The term FIA is also ambiguous outside image restoration. In time-series forecasting, "FIA-Net" denotes Frequency Information Aggregation, a hyper-complex STFT-window aggregation method (Yakir et al., 27 Feb 2025). In time-series explainability, FIA denotes Feature Importance Approximations within the SpectralX framework (Chung et al., 2024). These usages are unrelated to the Frequency Illumination Adaptor of RetinexDual. A common misconception is therefore to treat "FIA" as a stable acronym across domains; the literature shows that it is not.

RetinexDual’s stated limitation is broad: the model is "not optimized in terms of inference time and size" and still has difficulty with certain challenging images (Kishawy et al., 6 Aug 2025). FIA-specific limitations are more inferential. The use of global FFT with simple $\psi_d$5 convolutions may be sub-optimal for strongly spatially non-uniform illumination, because no explicit localized or multi-window frequency mechanism is defined. Likewise, illumination is modeled as feature maps without explicit physical constraints such as non-negativity or smoothness priors beyond what the network learns. The paper’s discussion suggests several future directions: more advanced frequency representations for illumination, including multi-window or block-wise FFT; wavelet or learned spectral bases that are localized in both space and frequency; improved efficiency; and possible extension to spatiotemporal modeling for video.

In the present literature, FIA is therefore best understood as a compact Fourier-domain illumination branch embedded in a Retinex decomposition, designed to exploit frequency-domain global context precisely where global illumination and color corruption dominate. Its significance lies not in spectral processing alone, but in the decision to confine that processing to illumination while delegating localized structural restoration to a spatial reflectance branch (Kishawy et al., 6 Aug 2025).