CSWM: Cross-Scale Wavelet Mamba in DEPF

• CSWM is a low-frequency enhancement module that boosts global brightness and coarse structures in low-light UAV RGB images using 2D Haar wavelet decomposition.
• It employs multi-scale depthwise convolutions and bidirectional Mamba-based state-space modeling to adaptively re-weight the LL component for improved brightness.
• Operating within DEPF, CSWM complements Fourier-based detail recovery to enable efficient multispectral fusion and robust object detection on UAV platforms.

Cross-Scale Wavelet Mamba (CSWM) is the low-frequency enhancement block inside the Dual-Domain Enhancement (DDE) module of DEPF, a UAV multispectral object detector with dual-domain enhancement and priority-guided mamba fusion. It operates on the low-frequency component $LL$ of low-light RGB UAV images obtained by a 2D discrete wavelet transform, and uses a Mamba-based cross-scale scanning mechanism to enhance global brightness and overall structural information. Within DEPF, CSWM is paired with the Fourier Details Recovery block (FDR): CSWM targets low-frequency brightness and structure, while FDR targets high-frequency texture and detail. The enhanced RGB image is then used together with infrared features in the Priority-Guided Mamba Fusion module and the $\text{S}^2\text{ANet}$ detection head (Li et al., 9 Sep 2025).

1. Definition and placement within DEPF

DEPF is proposed for multispectral remote sensing object detection on UAV platforms under three stated constraints: low-light remote sensing images reduce complementarity during multi-modality fusion, local small target modeling is easily interfered with by redundant information in the fusion stage, and transformer-based methods are difficult to apply on UAV platforms because of quadratic computational complexity. CSWM addresses the first of these constraints by enhancing the low-frequency content of low-light RGB imagery through a linear-time selective state-space model rather than self-attention (Li et al., 9 Sep 2025).

Within this detector, the DDE module is explicitly decomposed as

$\text{DDE} = \text{CSWM} + \text{FDR},$

with CSWM operating in the wavelet domain and FDR operating in the Fourier domain. The design rationale is stated directly: low-light degradation mainly suppresses low-frequency energy, corresponding to global brightness and coarse structures, whereas high-frequency parts still contain some texture but are less dominant. CSWM therefore models only the low-frequency component using Mamba, with the aim of improving low-light RGB quality in a way that is beneficial for multispectral detection rather than performing generic image enhancement (Li et al., 9 Sep 2025).

A common misconception is to treat CSWM as the full enhancement system. In DEPF, it is only the low-frequency branch of DDE. Texture-details are handled by FDR, fusion is handled by PGMF, and final oriented object detection is handled by $\text{S}^2\text{ANet}$ (Li et al., 9 Sep 2025).

2. Wavelet-domain formulation and recursive reconstruction

CSWM begins from an input low-light RGB image

$I_v \in \mathbb{R}^{B \times C \times H \times W},$

to which an $N$-level 2D Haar wavelet transform is applied: $$LL,\left[ HL,LH,HH \right] _n,...,\left[ HL,LH,HH \right] _1=DWT\left( I_v \right).$$ Here, $LL$ is the multi-level low-frequency component at the coarsest scale, and $\left[HL,LH,HH\right]_k$ are the horizontal, vertical, and diagonal high-frequency components at level $k$. The implementation uses the Haar basis with $\text{S}^2\text{ANet}$0 (Li et al., 9 Sep 2025).

CSWM enhances only the $\text{S}^2\text{ANet}$1 component. The high-frequency bands are forwarded with a simple MLP before inverse wavelet reconstruction. After low-frequency enhancement, reconstruction is written as

$\text{S}^2\text{ANet}$2

If the current level $\text{S}^2\text{ANet}$3 is not the last DWT level, the reconstructed $\text{S}^2\text{ANet}$4 is fed again into CSWM for the next level, forming a coarse-to-fine enhancement process (Li et al., 9 Sep 2025).

This recursive structure is important for interpreting the module. The low-frequency component is enhanced at the coarsest approximation level, but reconstruction is not terminal after a single pass. Instead, the module uses inverse wavelet reconstruction to re-enter the enhancement path, which preserves the paper’s emphasis on progressive brightness normalization rather than one-shot frequency modulation (Li et al., 9 Sep 2025).

3. Internal architecture and the meaning of “cross-scale”

The internal CSWM pipeline is described as four stages: multi-scale spatial feature extraction from $\text{S}^2\text{ANet}$5, global feature aggregation, cross-scale sequence construction with bidirectional scanning, and Mamba-based sequence modeling followed by re-weighting of $\text{S}^2\text{ANet}$6 (Li et al., 9 Sep 2025).

From the low-frequency input $\text{S}^2\text{ANet}$7, three depthwise convolutions are applied: $\text{S}^2\text{ANet}$8 These yield $\text{S}^2\text{ANet}$9, $\text{DDE} = \text{CSWM} + \text{FDR},$0, and $\text{DDE} = \text{CSWM} + \text{FDR},$1, corresponding to three receptive-field scales. A global descriptor is then computed by global average pooling: $\text{DDE} = \text{CSWM} + \text{FDR},$2 Each scale feature is flattened and combined with the flattened global descriptor: $\text{DDE} = \text{CSWM} + \text{FDR},$3 To emulate bidirectional modeling, the paper forms

$\text{DDE} = \text{CSWM} + \text{FDR},$4

where $\text{DDE} = \text{CSWM} + \text{FDR},$5 denotes reversal along the token dimension (Li et al., 9 Sep 2025).

The phrase “cross-scale” has a specific meaning in this formulation. It does not denote arbitrary multilevel processing over all wavelet subbands. Instead, it combines two scale notions. First, three spatial scales are induced by the $\text{DDE} = \text{CSWM} + \text{FDR},$6, $\text{DDE} = \text{CSWM} + \text{FDR},$7, and $\text{DDE} = \text{CSWM} + \text{FDR},$8 depthwise convolutions. Second, a shared global feature $\text{DDE} = \text{CSWM} + \text{FDR},$9 is injected into each scale-specific sequence after flattening, so each serialized sequence carries both local scale-specific structure and global context. The Mamba selective state-space model is then applied independently to each scale-specific sequence, and the results are aggregated (Li et al., 9 Sep 2025).

The Mamba layer is described in the paper through the standard state-space formalism associated with Gu and Dao: $\text{S}^2\text{ANet}$0 The practical significance is that the sequence model has linear time complexity with respect to sequence length, in contrast to quadratic self-attention. After sequence modeling, the three scale outputs are summed and used to modulate the original low-frequency tensor: $\text{S}^2\text{ANet}$1 The output $\text{S}^2\text{ANet}$2 is therefore a multiplicatively re-weighted low-frequency representation, where the gain map is learned from multi-scale context and global sequence dependencies (Li et al., 9 Sep 2025).

A second misconception concerns this “cross-scale” label. In DEPF, it refers specifically to the interaction among the three convolutional receptive-field scales and the shared global descriptor, not to a separate cross-attention mechanism across full-resolution RGB and infrared streams (Li et al., 9 Sep 2025).

4. Functional role: brightness enhancement and dual-domain complementarity

The paper characterizes low-frequency components as encoding global illumination or brightness, coarse structures, and low-frequency color variations. On that basis, the modulation

$\text{S}^2\text{ANet}$3

is interpreted as an adaptive, spatially varying brightness gain. Regions where the modulation exceeds $\text{S}^2\text{ANet}$4 are amplified; regions where it is less than $\text{S}^2\text{ANet}$5 are suppressed. This mechanism is used to compensate underexposure and uneven illumination in low-light UAV RGB imagery while preserving structural relationships (Li et al., 9 Sep 2025).

The functional objective is not merely photometric enhancement. DEPF is a multispectral detector, and CSWM is designed to improve the complementary value of RGB relative to infrared. Without enhancement, the paper states that low-light RGB images have very weak features compared to infrared, so RGB may contribute less useful information and can even harm fusion through modality imbalance. CSWM is intended to equalize and enhance RGB brightness so that RGB features become more informative for subsequent multispectral fusion (Li et al., 9 Sep 2025).

The paper also states that low-frequency enhancement alone does not fully restore texture-details. This is why CSWM is coupled with FDR in the DDE module. FDR takes the intermediate reconstructed image $\text{S}^2\text{ANet}$6, computes Fourier amplitude and phase,

$\text{S}^2\text{ANet}$7

enhances them via Spectrum Recovery Networks, and reconstructs the final enhanced image $\text{S}^2\text{ANet}$8 through inverse FFT (Li et al., 9 Sep 2025).

This separation of responsibilities is central to the design. CSWM handles brightness and global structure in the wavelet low-frequency branch, whereas FDR handles detail and texture in the Fourier branch. A plausible implication is that DEPF treats low-light enhancement as a factorized inverse problem: illumination and coarse structure are addressed in the wavelet approximation space, while texture recovery is addressed in the spectral amplitude-phase space. The paper itself makes the more limited claim that both brightness enhancement and detail recovery are necessary for improved detection (Li et al., 9 Sep 2025).

5. Efficiency, ablation behavior, and detector-level evidence

The efficiency argument for CSWM follows directly from the use of Mamba. The paper relies on the established property that Mamba has $\text{S}^2\text{ANet}$9 time complexity in sequence length $I_v \in \mathbb{R}^{B \times C \times H \times W},$0, versus $I_v \in \mathbb{R}^{B \times C \times H \times W},$1 for transformer self-attention. In CSWM, each serialized feature $I_v \in \mathbb{R}^{B \times C \times H \times W},$2 has length $I_v \in \mathbb{R}^{B \times C \times H \times W},$3, and the three scales are processed independently, so total complexity is proportional to $I_v \in \mathbb{R}^{B \times C \times H \times W},$4 (Li et al., 9 Sep 2025).

At the detector level, DEPF is compared with transformer-based multispectral detectors. The paper reports the following values:

Method	Params (MB)	FLOPs (G) / FPS
TSFADet	104.7	109.8 / 19
$I_v \in \mathbb{R}^{B \times C \times H \times W},$5Former	118.5	115.6 / 11
DMM	88.1	108.8 / 17
DEPF	80.3	108.3 / 16

The accompanying interpretation is specific. DEPF, which includes DDE and thus CSWM, uses fewer parameters and slightly fewer FLOPs than the transformer-based $I_v \in \mathbb{R}^{B \times C \times H \times W},$6Former, while improving accuracy. Its FPS is slightly lower than DMM because the 2D-DWT and FFT operations in DDE have no trainable parameters but do incur computational cost. The role attributed to CSWM in this comparison is that the linear-time SSM helps keep overall complexity reasonable for UAV deployment (Li et al., 9 Sep 2025).

The ablation study on DroneVehicle clarifies the contribution of CSWM relative to FDR and PGMF:

Variant	mAP@0.5	[email protected]:0.95
Baseline, no DDE	77.8	49.7
PGMF only, no DDE	78.1	50.8
CSWM only	77.8	50.0
FDR only	75.4	49.1
CSWM + FDR	78.3	50.7
Full DEPF	78.9	51.2

These results support several narrow conclusions. CSWM alone does not significantly improve [email protected] over the baseline, though it slightly improves [email protected]:0.95. FDR alone degrades performance. CSWM and FDR together yield gains over the baseline, and the full combination with PGMF reaches the best performance (Li et al., 9 Sep 2025).

This ablation addresses another common misunderstanding: CSWM is not presented as a standalone sufficient solution. The empirical evidence in DEPF instead assigns it an enabling role within a three-part pipeline. CSWM provides essential global brightness enhancement, FDR complements it with detail recovery, and PGMF exploits the resulting RGB features during multispectral fusion (Li et al., 9 Sep 2025).

6. Implementation details and training context

The implementation-specific description of CSWM is concise but concrete. The wavelet basis is Haar, with a 2-level 2D-DWT. Low-frequency processing uses three depthwise convolutions with kernel sizes $I_v \in \mathbb{R}^{B \times C \times H \times W},$7, $I_v \in \mathbb{R}^{B \times C \times H \times W},$8, and $I_v \in \mathbb{R}^{B \times C \times H \times W},$9, followed by global average pooling to obtain $N$0. Sequence formation consists of flattening across spatial dimensions, addition with flattened $N$1, and use of forward plus reversed sequences for bidirectional scanning. The state-space layer is implemented via Vision-Mamba building blocks, though exact hyperparameters are not enumerated in the text (Li et al., 9 Sep 2025).

Reconstruction uses an MLP on the high-frequency components before IDWT. The enhanced image $N$2 is reconstructed for each level and then either passed into another CSWM+FDR stage if the current level is not the last DWT level, or forwarded as the final enhanced image to the backbone. The detector is trained end-to-end, and there are no special loss terms dedicated solely to CSWM. The full model uses

$N$3

where $N$4 is cross-entropy classification loss and $N$5 is Smooth L1 regression loss (Li et al., 9 Sep 2025).

The end-to-end pipeline is correspondingly structured. Raw low-light RGB $N$6 and infrared images are input; DDE performs DWT, CSWM enhancement of $N$7, IDWT-based reconstruction, and Fourier-based detail recovery; a Vision-Mamba backbone extracts features from enhanced RGB and infrared images; PGMF fuses the modality features; and $N$8 performs oriented object detection (Li et al., 9 Sep 2025).

7. Position within wavelet–SSM research

CSWM, in its exact terminology, is defined in DEPF. However, related work shows a broader research pattern in which wavelet-domain decomposition is paired with state-space modeling or Mamba for global context capture. W-Mamba integrates wavelet transform with the state-space model for infrared and visible image fusion and introduces a Wavelet-SSM module together with cross-modal feature attention modulation (Zhang et al., 24 Mar 2025). WaveSeg uses wavelet-domain decomposition in a segmentation decoder, with Mamba-based state space modeling on high-frequency branches and reparameterized convolutions to preserve low-frequency semantic integrity (Xu et al., 24 Oct 2025). WaMaIR combines Global Multiscale Wavelet Transform Convolutions with a Mamba-Based Channel-Aware Module for image restoration (Zhu et al., 19 Oct 2025). DiMSUM incorporates wavelet transformation into Mamba for diffusion models and fuses wavelet-based outputs with spatial Mamba outputs through a cross-attention fusion layer (Phung et al., 2024). WDMamba decomposes image dehazing into low-frequency restoration with Vision Mamba followed by detail enhancement, guided by the observation that haze-related information predominantly resides in low-frequency components (Sun et al., 7 May 2025).

This suggests that CSWM belongs to a larger methodological family in which wavelet subbands are used to separate coarse structure from detail, and SSM-based modules are used where global or long-range dependencies are most valuable. DEPF’s formulation is narrower and more task-specific than several of these related systems. Its CSWM is tailored to UAV multispectral detection, operates only on the low-frequency $N$9 component of low-light RGB imagery, and is embedded in a detector-centric architecture that also includes PGMF and $$LL,\left[ HL,LH,HH \right] _n,...,\left[ HL,LH,HH \right] _1=DWT\left( I_v \right).$$0 (Li et al., 9 Sep 2025).

Relative to transformer-based enhancement or fusion, the DEPF paper positions CSWM as a linear-time alternative to cross-attention-heavy designs such as $$LL,\left[ HL,LH,HH \right] _n,...,\left[ HL,LH,HH \right] _1=DWT\left( I_v \right).$$1Former. Relative to pure CNN-based enhancement, CSWM is presented as adding global, long-range modeling via Mamba. Relative to other frequency-domain methods, DEPF distinguishes its dual-domain split between wavelet low-frequency enhancement and Fourier amplitude-phase detail recovery (Li et al., 9 Sep 2025).

In this specific sense, Cross-Scale Wavelet Mamba is best understood not as a generic synonym for any wavelet–Mamba block, but as a defined low-frequency enhancement module whose technical identity comes from four coupled choices: 2D Haar wavelet decomposition of low-light RGB input, multi-scale depthwise convolution with shared global pooling, bidirectional sequence serialization for Vision-Mamba-style SSM processing, and multiplicative re-weighting of the $$LL,\left[ HL,LH,HH \right] _n,...,\left[ HL,LH,HH \right] _1=DWT\left( I_v \right).$$2 component before recursive reconstruction and downstream multispectral fusion (Li et al., 9 Sep 2025).