MoWE: Spatially Adaptive Mixture-of-Wavelet-Experts Pooling for Ultrasound Lesion Segmentation

We present Mixture-of-Wavelet-Experts (MoWE), a spatially adaptive routing mechanism that replaces max-pooling and strided convolutions in U-Net architectures for ultrasound lesion segmentation. Standard pooling operations suppress high-frequency spatial details, including potential boundary cues in speckled regions. Recent frequency-domain methods preserve some of these details, but a single wavelet family applies the same spectral bias across the image. MoWE instead uses a context-aware router to assign local regions to fixed wavelet families according to local texture and global feature context. The decoder reuses the encoder's spatial routing maps during the inverse transform. Learnable channel-wise gates rescale the high-frequency subbands before reconstruction. We evaluate MoWE with U-Net on four ultrasound lesion benchmarks (BUSI, TN3K, UDIAT, BUS-UCLM) and one cardiac dataset (CAMUS), and with nnU-Net on BUSI. On BUSI, MoWE improves U-Net Dice from 72.59\% to 74.55\% and reduces HD95 from 47.01 to 43.49\,px. With nnU-Net, MoWE improves Dice from 80.18\% to 81.97\% and reduces ASSD from 20.07 to 17.25\,px. On U-Net, MoWE reduces trainable parameters by 6.4\%.