Frequency-Decoupled Image Deblurring

• Frequency-decoupled image deblurring is a technique that separates low- and high-frequency components to specifically preserve broad structures and recover fine details.
• It employs diverse methods—such as wavelet subbands, Fourier/FRFT operators, and learned low-pass filters—integrated within multi-scale and transformer-based architectures.
• Recent approaches demonstrate significant improvements in metrics like PSNR and SSIM by combining kernel priors, adaptive frequency control, and diffusion sampling to balance restoration quality and artifact reduction.

Frequency-decoupled image deblurring denotes a class of deblurring methods that explicitly separate, reweight, or jointly optimize image information across frequency bands rather than treating a blurred image as an undifferentiated signal. In current work, this separation appears in several forms: low-/high-frequency decomposition, joint spatial-frequency processing, kernel-level modeling in Fourier space, and frequency-selective guidance for diffusion-based restoration. Taken together, these studies suggest that the central objective is to preserve low-frequency structure while restoring high-frequency edges, textures, and blur-specific spectral cues with mechanisms that are physically aligned with convolutional blur formation (Zhang et al., 2022, Kong et al., 2022, Xiao et al., 2024).

1. Signal-theoretic basis

The classical blur model is convolutional: a sharp image is convolved with a blur kernel and corrupted by noise. In Fourier form, the same process becomes multiplicative. One representative formulation writes

$B(\omega) = F(\omega)G(\omega) + N(\omega),$

where $B$ is the blurry image, $F$ the sharp image, $G$ the blur kernel, and $N$ noise. This formulation underlies much of the modern literature because it makes explicit that blur suppresses or alters particular frequency components, especially high frequencies associated with edges and fine details (Mao et al., 2021).

A recurring empirical observation is that blur primarily damages high-frequency information while low-frequency structure is comparatively less altered. That observation motivates explicit separation of restoration and denoising. In one-shot convolutional deblurring, the deblurring kernel is synthesized as a linear combination of Finite Impulse Response even-derivative filters to compensate the frequency fall-off of the Point Spread Function, while a Gaussian low-pass filter is used to decouple denoising from edge deblurring. The decoupled reconstruction is written as

$$\bar{f}_L(x)=h^{-1}_{PSF}(x)*h_{Denoise}(x)*f_B(x),$$

which makes the deblurring and denoising roles explicit (Hosseini et al., 2018).

A limitation of standard Fourier analysis is that it is tied to stationary signals. For non-stationary blur, this motivates transforms that mix spatial and frequency localization. F2former uses the Fractional Fourier Transform as a unified spatial-frequency representation and argues that it is better suited to non-stationary signals like images. This is the basis for its Fractional Fourier based Wiener deconvolution and its fractional frequency aware transformer block (Paul et al., 2024).

2. Forms of frequency decoupling

The literature does not converge on a single operator for frequency decoupling. Instead, several distinct mechanisms are used to split or control spectral content.

Mechanism	Representative methods	Core operation
Wavelet subbands	FAG-Loss (Xiao et al., 2024), MFENet (Xiang et al., 2024), CogSENet (Wang et al., 29 Jun 2026)	Decompose into $LL$, $LH$, $HL$, $HH$ or explicit low/high branches
Fourier multiplication	FFTFormer (Kong et al., 2022), FIM (Sun et al., 20 Apr 2025), DeepRFTv2 (Mao et al., 26 Nov 2025)	Replace spatial correlation or kernel application with element-wise spectral products
DCT window partitioning	LoFormer (Mao et al., 2024)	Split DCT coefficients into local low-/high-frequency windows
FRFT spatial-frequency representation	F2former (Paul et al., 2024)	Learn in a representation between pure spatial and pure frequency domains
Learned low-/high-pass separation	MSFS-Net (Zhang et al., 2022), SFAFNet (Gao et al., 20 Feb 2025)	OctConv-style or learnable low-pass filtering with explicit LF/HF branches
Adaptive positional frequency control	FrENet (Jiao et al., 30 May 2025)	Modulate spectral regions according to their positions in the frequency map
Sampling-time frequency curriculum	FGPS (Thaker et al., 2024)	Admit measurement frequencies progressively during diffusion restoration

Wavelet formulations are common when the objective is explicit subband supervision or feature routing. In the frequency-aware guidance loss for blind restoration, Haar-based 2D discrete wavelet transform decomposes the estimated degraded image into $B$0, $B$1, $B$2, and $B$3 bands, and the loss enforces spatial consistency together with high-frequency consistency:

$B$4

MFENet likewise uses Haar DWT in its Frequency Enhanced Blur Perception module, while CogSENet’s BiFreqFusionBlock decomposes features into low-frequency coefficients and high-frequency coefficients through orthogonal wavelet projection (Xiao et al., 2024, Xiang et al., 2024, Wang et al., 29 Jun 2026).

Other methods avoid fixed transforms and instead learn the separation itself. MSFS-Net uses a Frequency Separation Module based on Octave Convolution, with explicit exchange between low- and high-frequency branches. SFAFNet’s Frequency Domain Information Dynamic Generation Module generates a learnable low-pass filter and defines the high-frequency component by $B$5, thereby producing adaptive spatially variant low-/high-frequency decomposition (Zhang et al., 2022, Gao et al., 20 Feb 2025).

3. Architectural realizations

Frequency-decoupled deblurring is most often embedded in multi-scale encoder-decoder networks. In CNN-oriented designs, the decoupling is usually bound to scale-space processing. MSFS-Net inserts its Frequency Separation Module at each scale, applies cycle-consistency to retain low-frequency content, and uses a contrastive learning module to recover high-frequency information. MFENet combines a multi-scale feature extraction module based on depthwise separable convolutions with a Frequency Enhanced Blur Perception module that merges wavelet-derived high-frequency details and multi-strip pooling for non-uniform blur perception. AIBNet localizes spatially degraded regions with SFDHBlock and then selects the most informative high-frequency responses with HFSBlock, where the difference between sharp and blurred images is treated as lying primarily in the high-frequency components (Zhang et al., 2022, Xiang et al., 2024, Gao et al., 28 Feb 2025).

Transformer-based methods tend to shift the decoupling into attention and feed-forward operators. FFTFormer replaces spatial self-attention with the Frequency domain-based Self-Attention Solver,

$B$6

and augments the feed-forward stage with a JPEG-inspired Discriminative Frequency Domain-based FFN that learns which low- and high-frequency information should be preserved. LoFormer first maps features into the DCT domain, partitions coefficients into local frequency windows, and applies Local Channel-wise Self-Attention so that low-frequency structure and high-frequency detail are learned with separate local contexts. F2former moves beyond standard FT and uses FRFT in both its Wiener deconvolution module and its fractional frequency aware self-attention, while its FM-FFN splits high- and low-frequency features for separate refinement (Kong et al., 2022, Mao et al., 2024, Paul et al., 2024).

A third line of work centers on dual-domain fusion rather than a strict branchwise split. SFAFNet’s GSFFBlock includes a spatial domain information module, FDGM, and a gated fusion module combining GATE and CAM to reweight and fuse spatial, low-frequency, and high-frequency features. FrENet operates directly in the frequency domain for RAW-to-RAW deblurring, introduces Adaptive Frequency Positional Modulation to modulate spectral regions according to their positions, and adds frequency-domain skip connections to preserve high-frequency details. FSM-Net uses an FFT-based Frequency Attention branch in parallel with spatial processing and combines it with a Cross-Gated Vision E-Branchformer at the bottleneck, explicitly assigning high-frequency recovery and long-range dependency modeling to different subsystems (Gao et al., 20 Feb 2025, Jiao et al., 30 May 2025, Ly, 29 May 2026).

4. Kernel priors, blur physics, and blind deblurring

A major theme in frequency-decoupled deblurring is the recovery of kernel-level information rather than solely pixel-level residuals. A foundational observation is that simply applying ReLU in the frequency domain of a blur image and then performing inverse Fourier transform can reveal blur direction and blur level, implicitly exposing kernel pattern. On that basis, the Res FFT-ReLU Block inserts Fourier transform, ReLU, inverse Fourier transform, and $B$7 convolution into a residual block so that kernel-level and pixel-level cues are learned jointly (Mao et al., 2021).

This line develops further in blind deblurring with explicit kernel priors. Frequency-domain Learning with Kernel Prior for Blind Image Deblurring predicts a spatially varying kernel map and injects that prior into a frequency-based transformer through the Frequency Integration Module. Its fusion rule,

$B$8

is designed to combine image features and kernel features in the frequency domain, with multi-scale kernel injection and a training objective that includes both pixel and frequency losses (Sun et al., 20 Apr 2025).

DeepRFTv2 makes the kernel-level premise even more explicit. Its Fourier Kernel Estimator operates on decoder features rather than images, estimates kernels in Fourier space, multiplies them with the corresponding feature spectra, and transforms the result back to the spatial domain. The broader architecture is a decoupled multi-scale design with multiple hierarchical sub-unets and a reversible strategy, so scale-specific encoding and kernel-level correction are separated rather than entangled in a single stream (Mao et al., 26 Nov 2025).

For defocus deblurring, Frequency-Driven Inverse Kernel Prediction argues that spatial kernel estimation is unreliable in severely blurry regions because local high-frequency detail is missing. Its Dual-Branch Inverse Kernel Prediction predicts inverse-kernel amplitude from the amplitude spectrum and predicts phase with amplitude-guided attention, then reconstructs the inverse kernel for deconvolution. Position Adaptive Convolution uses only a limited set of predicted inverse kernels but adapts the receptive field by a learned dilation map, and the Dual-Domain Scale Recurrent Module fuses spatial and frequency processing from coarse to fine (Zhang et al., 18 Aug 2025).

5. Diffusion-based and sampling-time frequency control

Frequency decoupling also appears outside feed-forward architectures, especially in diffusion-based restoration. Frequency-Aware Guidance for Blind Image Restoration via Diffusion Models proposes a plug-and-play guidance loss that requires no retraining of pre-trained diffusion models. The method augments the spatial consistency term with DWT-based high-frequency constraints during reverse diffusion sampling. On blind image deblurring over FFHQ at $B$9, the reported PSNR rises from 22.24 to 25.96 for motion blur and from 24.77 to 26.23 for Gaussian blur, corresponding to improvements of up to $F$0 on motion blur and $F$1 on Gaussian blur over BlindDPS. The paper further reports that including all high-frequency bands yields the best PSNR, LPIPS, FID, and qualitative results, while overly large $F$2 causes artifacts and overly small $F$3 leads to over-smoothness (Xiao et al., 2024).

Frequency-Guided Posterior Sampling addresses a different issue: approximation error in diffusion posterior sampling for linear inverse problems. Its central claim is that existing guidance approximations can fail dramatically, especially when high-frequency constraints are imposed too aggressively. The remedy is a time-varying low-pass filter on the measurements,

$F$4

so that low frequencies are used early in the reverse process and higher frequencies are progressively admitted later. In motion deblurring on ImageNet, the reported results are FID $F$5, LPIPS $F$6, PSNR $F$7, and SSIM $F$8, compared with DPS at $F$9, $G$0, $G$1, and $G$2, respectively. This suggests that frequency decoupling can be imposed not only on features but also on the measurement curriculum used during sampling (Thaker et al., 2024).

6. Reported performance, recurring findings, and limitations

Across benchmarks, frequency-decoupled methods are reported to improve either restoration quality, efficiency, or both. Representative results include the following.

Method	Benchmark	Reported result
FFTFormer (Kong et al., 2022)	GoPro	PSNR 34.21 with 16.6M parameters
LoFormer-L (Mao et al., 2024)	GoPro	PSNR 34.09 dB with 126G FLOPs
F2former-L (Paul et al., 2024)	GoPro / HIDE	35.22 dB on GoPro and 33.48 dB on HIDE
AIBNet (Gao et al., 28 Feb 2025)	GoPro	PSNR 34.95 dB, SSIM 0.974
SFAFNet-B (Gao et al., 20 Feb 2025)	GoPro / RealBlur-R / DPDD	34.25 dB on GoPro, 40.83 dB on RealBlur-R, 26.79 dB on DPDD
FrENet+ (Jiao et al., 30 May 2025)	Deblur-RAW	PSNR 45.63 dB and SSIM 0.994
FAG-Diff (Xiao et al., 2024)	FFHQ $G$3	25.96 PSNR for motion blur and 26.23 for Gaussian blur

The qualitative claims are also highly consistent. FFTFormer reports sharper text, edges, and details than prior methods; MFENet reports improved recovery of license plate characters, vehicle contours, and fine structures, with LPIPS $G$4 and VIF $G$5 on GoPro; FrENet reports sharper detail and more natural texture recovery; and MFENet further reports downstream object detection improvement to $G$6 mean Average Precision versus $G$7 for the next-best deblurring method (Kong et al., 2022, Xiang et al., 2024, Jiao et al., 30 May 2025).

Several limitations and misconceptions recur. First, frequency-decoupled deblurring is not equivalent to indiscriminate high-frequency amplification. The diffusion guidance literature explicitly reports that excessive frequency weighting introduces artifacts, while insufficient weighting produces over-smoothness (Xiao et al., 2024). Second, Fourier-domain processing is not automatically sufficient for non-stationary blur; this is precisely the motivation for FRFT-based formulations (Paul et al., 2024). Third, the strongest reported systems are rarely frequency-only. They almost always preserve a spatial branch, a dual-domain bottleneck, or explicit cross-domain fusion, indicating that low-frequency structure, local spatial organization, and high-frequency restoration remain interdependent in practice (Gao et al., 20 Feb 2025, Ly, 29 May 2026). Finally, inverse-kernel prediction remains difficult in severely blurred regions, and using only a fixed small set of kernels introduces an expressivity-efficiency trade-off, even when adaptive dilation or recurrent fusion is added (Zhang et al., 18 Aug 2025).

Taken together, the literature suggests that frequency-decoupled image deblurring is best understood not as a single algorithmic family but as a design principle: isolate the spectral effects of blur, assign different operators to structure and detail, and fuse those components with enough spatial context to avoid artifacts and preserve semantics. Within that principle, wavelet subbands, DCT/FFT/FRFT operators, learned low-pass filters, kernel priors, and frequency-guided diffusion have emerged as the principal technical routes (Zhang et al., 2022, Mao et al., 2024, Sun et al., 20 Apr 2025).