Field seismic data often suffer from trace missing due to acquisition constraints. While deep learning has advanced reconstruction tasks, existing models often lack physical interpretability, risking geologically implausible results. To bridge this gap, we propose Seislet U-Net, which integrates forward and inverse Seislet transforms into a U-Net encoder-decoder. By leveraging local slope information to guide predictions along dominant seismic dips, this design enforces feature extraction and reconstruction in a physically consistent, sparse domain that aligns with seismic wavefront structures, thereby enhancing interpretability. Training uses a composite loss that balances sparsity, spatial smoothness, and structural fidelity. Experiments on synthetic and field datasets demonstrate that Seislet U-Net outperforms U-Net, denoising convolutional neural network, discrete wavelet transform U-Net, and AU-Net, achieving signal-to-noise ratio improvements of 1.47 dB and 4.49 dB, respectively, compared to U-Net. The framework integrates data-driven learning with domain-specific constraints, offering a reliable solution for seismic reconstruction.