A robust low‐rank tensor completion model with sparse noise for higher‐order data recovery

Abstract The tensor singular value decomposition‐based model has garnered increasing attention in addressing tensor recovery challenges. However, existing tensor recovery methods exhibit certain inherent limitations. Some ignore the simultaneous effects of noise and missing values, while most can't handle higher‐order tensors, which are not reflective of real‐world scenarios. The information redundancy within tensor data often leads to a prevailing low‐rank structure, making low‐rankness a vital prior in the tensor recovery process. To tackle this pressing issue, a robust low‐rank tensor recovery framework is proposed to rehabilitate higher‐order tensors corrupted by sparse noise and missing entries. In the model, the tensor nuclear norm derived for order‐ d tensors ( d 4) are employed as a representation of the low‐rank prior, while utilizing the ‐norm to model the sparse noise. To solve the proposed model, an efficient Alternating direction method of multipliers algorithm is developed. A series of experiments are performed on synthetic and real‐world datasets. The results show that the superior performance of the method compared with other algorithms dedicated to addressing order‐ d tensor recovery challenges. Notably, in scenarios where the data is severely compromised (noise ratio 40%, sample ratio 70%), the algorithm consistently outperforms its competitors, achieving significantly improved results.