Neutron imaging is essential for diagnosing and optimizing inertial confinement fusion implosions at the National Ignition Facility. Due to the required 10-micrometer resolution, however, neutron image require image reconstruction using iterative algorithms. For low-yield sources, the images may be degraded by various types of noise. Gaussian and Poisson noise often coexist within one image, obscuring fine details and blurring the edges where the source information is encoded. Traditional denoising techniques, such as filtering and thresholding, can inadvertently alter critical features or reshape the noise statistics, potentially impacting the ultimate fidelity of the iterative image reconstruction pipeline. However, recent advances in synthetic data production and machine learning have opened new opportunities to address these challenges. In this study, we present an unsupervised autoencoder with a Cohen-Daubechies- Feauveau (CDF 97) wavelet transform in the latent space, designed to suppress for mixed Gaussian-Poisson noise while preserving essential image features. The network successfully denoises neutron imaging data. Benchmarking against both simulated and experimental NIF datasets demonstrates that our approach achieves lower reconstruction error and superior edge preservation compared to conventional filtering methods such as Block-matching and 3D filtering (BM3D). By validating the effectiveness of unsupervised learning for denoising neutron images, this study establishes a critical first step towards fully AI-driven, end-to-end reconstruction frameworks for ICF diagnostics.