A two-step enhanced tensor denoising framework based on noise position prior and adaptive ring rank

Recently, low-rank tensor recovery has garnered significant attention. Its objective is to recover a clean tensor from an observation tensor that has been corrupted. However, existing methods typically do not exploit the prior information of the noise’s position, and methods based on tensor ring decomposition also require a preset rank. In this paper, we propose a framework that leverages this prior information to transform the denoising problem into a complementary one, ultimately achieving effective tensor denoising. This framework consists of two steps: first, we apply an efficient denoising method to obtain the noise prior and identify the noise’s positions; second, we treat these positions as missing values and perform tensor ring completion. In the completion problem, we propose a tensor ring completion model with an adaptive rank incremental strategy, effectively addressing the preset rank problem. Our framework is implemented using the alternating direction method of multipliers (ADMM). Our method has been demonstrated to be superior through extensive experiments conducted on both synthetic and real data.