DenoDet V2: Transform-Domain SAR Detector

• DenoDet V2 is a SAR object detector that denoises features in the transform domain by cross-modulating phase and amplitude to counteract speckle noise.
• It integrates a plug-and-play DFTDeno module into a ConvNeXt-Tiny backbone with an FPN and GFL head, enhancing detection in challenging SAR imagery.
• The method’s band-wise partition self-attention and token exchange yield improved mAP performance with reduced parameters and near-constant FLOPs.

DenoDet V2 is a SAR object detector that performs feature denoising in the transform domain rather than relying solely on spatial-domain analysis or enhancement. Introduced in "DenoDet V2: Phase-Amplitude Cross Denoising for SAR Object Detection" (Ni et al., 12 Aug 2025), it is designed for Synthetic Aperture Radar imagery, where coherent speckle noise degrades target–background contrast and introduces spurious high-frequency artifacts. The method augments a one-stage detector by inserting a plug-and-play DFTDeno module into the backbone and exploits the complementary nature of amplitude and phase information through a band-wise mutual modulation mechanism, enabling reciprocal enhancement between phase and amplitude spectra.

1. Problem setting and design rationale

Synthetic Aperture Radar imagery is inherently contaminated by coherent speckle noise, described as a multiplicative, high-frequency noise resulting from coherent processing of backscattered signals. In object detection, this noise degrades contrast between target and background, especially for small and medium objects, and produces spurious high-frequency artifacts that mislead spatial-domain convolutional features (Ni et al., 12 Aug 2025).

The method is positioned against two established tendencies in SAR denoising. Traditional approaches either operate purely in the spatial domain, including filtering and CNN-based despeckling, or apply frequency-domain transforms while treating amplitude and phase independently. DenoDet V2 is defined by rejecting that separation: amplitude $A$ is described as highly sensitive to speckle noise, whereas phase $\Phi$ encodes structural information and is relatively robust to noise. Its central premise is that denoising should be formulated as cross-spectral feature modulation in the frequency domain, with amplitude and phase mutually guiding one another.

This framing distinguishes DenoDet V2 from methods that use spatial-domain characteristics for implicit denoising. A plausible implication is that the model treats SAR noise not merely as a nuisance to be suppressed after feature extraction, but as a phenomenon whose spectral structure can be leveraged during representation learning.

2. Detector composition and integration into the backbone

DenoDet V2 augments a one-stage base detector, GFL, by inserting a plug-and-play DFTDeno module into the backbone. The stated pipeline is:

$$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$

The implementation uses a ConvNeXt-Tiny backbone with an FPN and a GFL head (Ni et al., 12 Aug 2025). The DFTDeno module is inserted after stage 3 of the backbone and before lateral connections. This placement indicates that the transform-domain operation is applied to intermediate semantic features rather than raw pixels or final multi-scale features.

The broader detector lineage is explicit in the paper’s references. The detection head follows X. Li et al., "Generalized Focal Loss," NeurIPS 2020, while the evaluation spans SARDet-100K from Y. Li et al., SAR-AIRcraft-1.0 from Z. Wang et al., and AIR-SARShip-1.0 from X. Sun et al. DenoDet V2 is also presented as the successor to Y. Dai et al.’s DenoDet: "Attention as Deformable Multi-Subspace Feature Denoising," TAES 2024.

3. Transform-domain decomposition and phase–amplitude mutual modulation

Given an intermediate feature map $\mathbf{M}\in\mathbb{R}^{C\times H\times W}$, DFTDeno first applies a 2D Discrete Fourier Transform:

$$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$

The transformed feature is decomposed into real and imaginary parts:

$$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$

Amplitude and phase are then extracted as

$$A_{c,u,v} =\sqrt{\mathcal{R}_{c,u,v}^2+\mathcal{I}_{c,u,v}^2},\quad \Phi_{c,u,v} =\mathrm{atan2}\bigl(\mathcal{I}_{c,u,v},\,\mathcal{R}_{c,u,v}\bigr)\in[-\pi,\pi).$$

To avoid angular wrapping, phase is represented as a 2-channel unit vector $\bigl(\cos\Phi,\sin\Phi\bigr)$. This representation is important in the reported ablations, where phase angle decomposition by orthogonal split and trigonometric realignment yields $+0.6$ mAP relative to naïve angle regression.

The denoising operation is driven by an attention map $\mathbf{G}\in\mathbb{R}^{H\times W}$ that jointly depends on amplitude and phase and is applied to both modalities:

$\Phi$0

where $\Phi$1 denotes element-wise multiplication. The novelty is that $\Phi$2 is produced by cross-spectral self-attention in local frequency bands rather than by independent per-modality processing (Ni et al., 12 Aug 2025).

4. Band-wise partition self-attention and token exchange

The attention construction begins with channel pooling. For a frequency-domain tensor $\Phi$3, the channel dimension is collapsed by max-plus-average pooling:

$\Phi$4

producing $\Phi$5.

The pooled map is partitioned into non-overlapping bands of size $\Phi$6, generating $\Phi$7 groups. Within each band, DenoDet V2 applies Band-Wise Partition Self-Attention, or BPSA. Each band uses linear projections to produce $\Phi$8, $\Phi$9, and $$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$0, followed by self-attention with a learnable positional encoding $$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$1, and then aggregation across bands with an MLP whose hidden layer has size $$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$2. The resulting $$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$3 becomes the attention map $$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$4.

The defining extension beyond DenoDet V1 is the phase–amplitude token exchange. For the $$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$5-th band, the amplitude branch uses queries from amplitude and keys/values from phase:

$$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$6

while the phase branch uses queries from phase and keys/values from amplitude:

$$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$7

The attention outputs $$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$8 and $$\text{Input image} \rightarrow \text{Backbone conv-stages} \rightarrow \text{DFTDeno (per feature map)} \rightarrow \text{FPN neck} \rightarrow \text{GFL head} \rightarrow \text{Detection outputs}.$$9 are recombined across bands, and the final attention map is formed as

$\mathbf{M}\in\mathbb{R}^{C\times H\times W}$0

In the comparison provided by the authors, DenoDet V1 performs soft-thresholding attenuation in the frequency domain via deformable subspaces, whereas DenoDet V2 replaces this with a dual-modal, band-wise cross-attention, identified as PATE, between amplitude and phase. This suggests a shift from attenuation-oriented denoising to modulation-oriented denoising.

After modulation, the complex spectrum is reconstructed as

$\mathbf{M}\in\mathbb{R}^{C\times H\times W}$1

and inverse DFT yields the recovered feature map:

$\mathbf{M}\in\mathbb{R}^{C\times H\times W}$2

The real part of $\mathbf{M}\in\mathbb{R}^{C\times H\times W}$3 is passed downstream.

5. Optimization, preprocessing, and training protocol

DenoDet V2 is trained end-to-end with the standard GFL detection losses (Ni et al., 12 Aug 2025). The loss is described in prose rather than by an auxiliary denoising objective: $\mathbf{M}\in\mathbb{R}^{C\times H\times W}$4 is a Quality Focal Loss on classification scores, and $\mathbf{M}\in\mathbb{R}^{C\times H\times W}$5 is a Distribution Focal Loss plus IoU-aware regression loss on bounding-box offsets. No explicit auxiliary denoising or modulation consistency losses are used; the DFTDeno module learns through backpropagation from the detection loss alone.

The input preprocessing resizes images to $\mathbf{M}\in\mathbb{R}^{C\times H\times W}$6 and applies random horizontal flip with probability $\mathbf{M}\in\mathbb{R}^{C\times H\times W}$7. For large SAR scenes, specifically SAR-Aircraft and AIR-SARShip, images are tiled into $\mathbf{M}\in\mathbb{R}^{C\times H\times W}$8 chips with $\mathbf{M}\in\mathbb{R}^{C\times H\times W}$9 px overlap. Optimization uses DAdaptAdam with initial learning rate $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$0 and weight decay $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$1. Training runs for 12 epochs with batch size 16 across $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$2 RTX 4090 GPUs, with gradient clipping at norm $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$3 and synchronized BatchNorm.

The band partition stride is set to $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$4, identified as the best trade-off from Tab. 4, and the hidden dimension in attention is $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$5. Positional encoding $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$6 is learned per band. A potential point of confusion is whether transform-domain denoising requires a separate restoration target; in this system it does not, because the denoising behavior is optimized purely through detection supervision.

6. Reported empirical performance, ablations, and interpretation

The experimental evaluation covers three SAR datasets. SARDet-100K contains 116,598 images and 6 object classes with an $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$7 split. SAR-Aircraft-1.0 contains 3,489 train and 879 test images across 7 classes. AIR-SARShip-1.0 consists of 31 large scenes with 4,611 ship instances. The reported metrics are standard COCO mAP at $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$8, together with $$\mathbf{m}_{c,u,v} =\sum_{h=0}^{H-1}\sum_{w=0}^{W-1} M_{c,h,w}\,e^{-2\pi i\bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\bigr)}.$$9 and $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$0 (Ni et al., 12 Aug 2025).

Setting	Reported result	Notes
GFL baseline on SARDet-100K	55.01% mAP	32.3 M params, 52.36 G FLOPs
DenoDet V1 on SARDet-100K	55.88% mAP	65.8 M params
DenoDet V2 on SARDet-100K	56.71% mAP	32.6 M params, 52.47 G FLOPs
DenoDet V2 on SAR-Aircraft-1.0 / AIR-SARShip-1.0	69.93% / 73.98% AP	surpassing all competitors by $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$1, with only $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$2 M parameters

On SARDet-100K, DenoDet V2 improves over DenoDet V1 by $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$3 mAP and over the GFL baseline by $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$4 mAP, while using roughly half the parameters of DenoDet V1 and keeping FLOPs nearly unchanged. The comparison to DenoDet V1 is summarized in the paper as a $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$5 mAP gain on SARDet-100K, a reduction from $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$6 M to $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$7 M parameters, and nearly unchanged FLOPs.

The ablation studies isolate the contributions of the transform-domain design. Modulating only amplitude yields $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$8 mAP, modulating only phase yields $$\mathcal{R}_{c,u,v} =\sum_{h,w}M_{c,h,w}\cos2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr),\quad \mathcal{I}_{c,u,v} =-\sum_{h,w}M_{c,h,w}\sin2\pi\Bigl(\tfrac{u\,h}{H}+\tfrac{v\,w}{W}\Bigr).$$9 mAP, and modulating both yields $$A_{c,u,v} =\sqrt{\mathcal{R}_{c,u,v}^2+\mathcal{I}_{c,u,v}^2},\quad \Phi_{c,u,v} =\mathrm{atan2}\bigl(\mathcal{I}_{c,u,v},\,\mathcal{R}_{c,u,v}\bigr)\in[-\pi,\pi).$$0, rising to $$A_{c,u,v} =\sqrt{\mathcal{R}_{c,u,v}^2+\mathcal{I}_{c,u,v}^2},\quad \Phi_{c,u,v} =\mathrm{atan2}\bigl(\mathcal{I}_{c,u,v},\,\mathcal{R}_{c,u,v}\bigr)\in[-\pi,\pi).$$1 with token exchange. The reported interpretation is that phase is more robust and that cross-modal denoising is synergistic. The band-wise partition stride performs best at $$A_{c,u,v} =\sqrt{\mathcal{R}_{c,u,v}^2+\mathcal{I}_{c,u,v}^2},\quad \Phi_{c,u,v} =\mathrm{atan2}\bigl(\mathcal{I}_{c,u,v},\,\mathcal{R}_{c,u,v}\bigr)\in[-\pi,\pi).$$2 bands, reaching $$A_{c,u,v} =\sqrt{\mathcal{R}_{c,u,v}^2+\mathcal{I}_{c,u,v}^2},\quad \Phi_{c,u,v} =\mathrm{atan2}\bigl(\mathcal{I}_{c,u,v},\,\mathcal{R}_{c,u,v}\bigr)\in[-\pi,\pi).$$3 mAP, and token exchange contributes an additional $$A_{c,u,v} =\sqrt{\mathcal{R}_{c,u,v}^2+\mathcal{I}_{c,u,v}^2},\quad \Phi_{c,u,v} =\mathrm{atan2}\bigl(\mathcal{I}_{c,u,v},\,\mathcal{R}_{c,u,v}\bigr)\in[-\pi,\pi).$$4 mAP over no-exchange cross-attention.

The qualitative analysis is consistent with the quantitative findings. Eigen-CAM heatmaps show that DenoDet V2 concentrates on true object regions and suppresses noise, while detection examples show fewer false alarms in clutter and improved recall on small or occluded targets. A plausible implication is that the attention-guided coupling of phase and amplitude does not merely suppress background responses globally; it also improves localization selectivity under SAR-specific clutter conditions.

The released implementation is available at the GrokSAR repository: https://github.com/GrokCV/GrokSAR.