Leveraging intrinsic data priors is critical for effective data recovery. However, existing approaches often struggle to simultaneously achieve theoretical guarantees, strong performance, and computational efficiency. In this paper, we introduce a novel \emph{Representative Coefficient Correlated Total Variation} (RCCTV) regularizer that captures the recently observed low-rank and local smoothness properties of the representative coefficient tensor derived from a low-rank decomposition. RCCTV offers three key advantages: (1) it operates on a compact representative coefficient image significantly smaller than the original data, enabling highly efficient optimization; (2) it jointly enforces low-rankness and spatial smoothness through a single regularizer, eliminating the need for trade-off parameters; and (3) when integrated into a robust PCA framework (RCCTV-RPCA), it admits provable exact recovery under mild conditions. To solve the resulting model, we develop an efficient ADMM-based algorithm accelerated via fast Fourier transform. Extensive experiments on both synthetic and real-world datasets demonstrate that RCCTV-RPCA achieves state-of-the-art accuracy with significantly reduced runtime.