Spatial heterodyne spectroscopy is a novel Fourier transform interferometric spectroscopy technique that achieves high spectral resolution within a specific wavelength range. It has been widely used in fields like atmospheric remote sensing, astronomical observation, and mineral detection. When applied to remote sensing of targets with continuous spectra, the resulting spatial heterodyne interferogram displays only a few interference fringes, yet contains rich spectral information. However, due to interference from complex environments and electronic components, the spatial heterodyne spectrometer may encounter noisy signals during target detection, leading to the destruction of the collected interference fringes. As a result, the spectral features are obscured by various types of noise, making it difficult to obtain valuable research data during the inversion process. As remote sensing research advances, effective methods to reduce the impact of noise on the information contained in continuous light spatial heterodyne interferograms are increasingly needed.Based on the principles of spatial heterodyne spectroscopy, a deep convolutional neural network is constructed using a residual learning approach to predict Gaussian noise, combined with batch normalization to accelerate training and improve network performance (Fig.2). By subtracting the predicted Gaussian noise from the noisy continuous light spatial heterodyne interferogram, the corresponding denoised interferogram is obtained. The effectiveness and superiority of this method are validated through comparisons with other denoising methods using visual effects, PSNR, SSIM, and spectral differences. By comparing the denoising performance of deep convolutional neural networks with different numbers of layers, the study provides effective suggestions for constructing and optimizing the network architecture.The SHI-DnCNN (Spatial heterodyne interferograms-Denoise convolutional neural networks) was constructed and trained, which is capable of denoising continuous light spatial heterodyne interferograms with varying Gaussian noise intensities and effectively restoring their spectra (Fig.3-Fig.6). To more accurately evaluate the denoising performance of SHI-DnCNN, comparisons were made with BM3D (Block-matching and 3D filtering), WNNM (Weighted nuclear norm minimization), TNRD (Trainable Nonlinear Reaction Diffusion), and CSC (Convolutional Sparse Coding). The results demonstrate that SHI-DnCNN outperforms the other algorithms in terms of visual quality, PSNR, SSIM, and spectral differences (Fig.7 and Fig.8). Furthermore, the denoising performance of SHI-DnCNN with different depths was compared. Within the range of 12 to 20 layers, visual quality, PSNR, and SSIM improved as the number of layers increased, stabilizing between 20 and 23 layers. The spectral differences fluctuated between 12 and 20 layers but rapidly decreased, stabilizing between 20 and 22 layers, with a sudden increase at 23 layers (Fig.9-Fig.11). This suggests that increasing the network depth can improve the model's denoising performance, but this must be balanced with the increased training time and the potential for overfitting. Finally, the SHI-DnCNN model trained on GaoFen-5 data was used to denoise CO₂ spatial heterodyne interferograms. For interferograms with Sigma=5, the denoised spectral shape nearly completely restored the original spectral shape. For interferograms with Sigma=10 and Sigma=15, although the overall spectral restoration was slightly insufficient, the main spectral peaks were recovered (Fig.13 and Fig.14).A method for denoising continuous light spatial heterodyne interferograms using a deep convolutional neural network is proposed. The results show that SHI-DnCNN exhibits significant denoising capability for Gaussian noise, effectively repairing distortions in the interferograms and restoring the spectral information damaged by noise. Furthermore, the denoising performance of SHI-DnCNN was compared with that of BM3D, WNNM, TNRD, and CSC, demonstrating superiority of SHI-DnCNN in denoising Gaussian noise from continuous light spatial heterodyne interferograms. By comparing the visual effects, PSNR, SSIM, and spectral differences of SHI-DnCNN with different depths in denoising Gaussian noise from interferograms, this study reveals how to rationally design and optimize the network depth to improve the denoising performance. Finally, SHI-DnCNN was applied to denoise GF-5 data, and the results show that the method achieved certain denoising results in interferograms with complex spectral features. This study provides valuable insights for the application of deep learning in spatial heterodyne spectroscopy and serves as a reference for related denoising research.