Accurate characterization of picosecond broadband pulse signals is important for radio-frequency electronics, radar detection and high-speed communications. However, bandwidth-limited oscilloscopes attenuate high-frequency components, broaden rising edges, reduce peak amplitudes and introduce ringing distortion. Conventional regularized deconvolution relies heavily on manual parameter tuning and is vulnerable to noise, while Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) models suffer from long training time and insufficient capability to capture global temporal dependencies. Here we present a waveform reconstruction method integrating convolutional neural networks, Transformer and learnable physics-guided deconvolution constraints. The model simultaneously extracts local waveform details and models global temporal correlations, which improves training efficiency and noise robustness, and restores pulse rising edges, peak amplitudes and overall waveform morphology with higher precision. The proposed method offers a low-cost software solution to realize high-precision measurement of high-speed pulse signals without hardware upgrades.