Algorithm 1: Multi-Level Gabor Frequency Network

Input: Source image $I_s\in {\mathbb{R}}^{3\times H\times W}$; fractional order $\alpha$; angle set           $\Theta =\{0°,45°,90°,135°\}$; scale set $S=\{1,2,3,4\}$.     Output: Multi-level frequency-aware features $[F_1,F_2,F_3]$.    1 Stage 1: Patch Embedding and Local Frequency Encoding    2 $X_1\leftarrow \mathrm{PatchEmbed}\left(I_s\right)$;              // Extract low-level patches    3 $Y_1\leftarrow \mathrm{GaborFrequencyNet}\left(X_1\right)$    4    Apply fractional Gabor filters $G_{\alpha }(\theta ,s)$ to capture orientation–scale textures;    5    Fuse complex-domain features via Frequency Attention (FA):    6 $Y_1\leftarrow {\alpha }_1·\mathrm{FA}\left(G_{\alpha }\left(X_1\right)\right)+(1-{\alpha }_1)·G_{\alpha }\left(X_1\right)$    7 Stage 2: Mid-Level Aggregation    8 $X_2\leftarrow \mathrm{PatchMerging}\left(Y_1\right)$;          // Downsample and double channels    9 $Y_2\leftarrow \mathrm{GaborFrequencyNet}\left(X_2\right)$  10 Stage 3: High-Level Fusion  11 $X_3\leftarrow \mathrm{PatchMerging}\left(Y_2\right)$  12 $Y_3\leftarrow \mathrm{GaborFrequencyNet}\left(X_3\right)$  13 Feature Reshaping  14  $F_1\leftarrow \mathrm{Reshape}\left(Y_1\right)\in {\mathbb{R}}^{4096\times 128}$; $F_2\leftarrow \mathrm{Reshape}\left(Y_2\right)\in {\mathbb{R}}^{1024\times 256}$; $F_3\leftarrow \mathrm{Reshape}\left(Y_3\right)\in {\mathbb{R}}^{256\times 512}$  15 return  $[F_1,F_2,F_3]$