KC-3DGS: Kurtosis-Constrained Gaussian Splatting for High-Fidelity View Synthesis

3D Gaussian Splatting (3DGS) enables real-time novel view synthesis, but with sparse training views it produces floaters, color casts and oversmoothed regions at novel viewpoints. Pixel-space losses (L1, SSIM) do not prevent this: they constrain the total reconstruction error, not how it is distributed across scales. We propose KC-3DGS, which regularizes 3DGS with wavelet-domain statistics of natural images. It combines three terms: (1) a scale-weighted alignment of wavelet coefficients, (2) a supervised kurtosis loss that matches the heavy-tailed statistics of each subband to the ground truth, and (3) a supervised cross-band covariance loss that matches how oriented subbands co-occur. A simple analysis shows why each term is needed. Pixel losses cannot distinguish errors at different scales. Over-smoothing and floaters lower subband kurtosis, which only a supervised kurtosis loss penalizes. Cross-band covariance captures joint structure, such as corners, that per-band statistics miss. Because these statistics pool over image positions, they can supervise renders from pseudo cameras near the training views, where sparse-view artifacts arise; all terms start after densification, leaving the Gaussian set unchanged. With 12 training views on five benchmarks (MipNeRF360, Tanks&Temples, Deep-Blending, WRIVA-ULTRRA, MVImgNet), KC-3DGS improves perceptual metrics (PSNR, SSIM, LPIPS, DreamSim) on scenes, and as a plug-and-play regularizer it also improves three existing sparse-view 3DGS methods by up to 28.8% reduction in DreamSim and 1.59 dB increase in PSNR.