Seismic images are often severely affected by random noiseRandom noise and acquisition footprint noiseFootprint noise, which significantly degrade the quality of seismic data and make accurate interpretation of subsurface structures challenging. As a result, effective footprint noiseFootprint noise removal techniques have become a critical issue in seismic data processing. Although existing methods, such as frequency-domain filtering, time-frequency processing, and dictionary learning (DcL)Dictionary learning (DcL), have shown some success in denoising, these approaches typically treat 3D seismic data as 2D images, neglecting the inherent three-dimensional structural information within the data. To address this limitation, this paper proposes an innovative tensor-based denoising model—unidirectional total variationUnidirectional total variation (UTV) regularization combined with tensor low-rank approximation (UTV-TLRA)Tensor low-rank approximation (TLRA)—aimed at simultaneously mitigating both random noiseRandom noise and acquisition footprint noiseFootprint noise. In this instance, UTV penalization is employed to capture the directional and structural features of the collection process, allowing the seismic data to be effectively decomposed into clean signals and footprint noiseFootprint noise components. Additionally, the tensor nuclear norm (TNN)Tensor nuclear norm (TNN) is applied to impose low-rank constraints on third-order seismic tensors, effectively suppressing random noiseRandom noise. To solve the optimization problem in this model, we propose an efficient optimization approach utilizing the split Bregman iterationSplit Bregman iteration (SBI). Experimental results on both synthetic and field seismic data demonstrate that the proposed method significantly outperforms current leading denoising techniques in both quantitative and qualitative evaluations, offering improved recovery of the true subsurface structures in seismic images.