Inductive Convolution Nuclear Norm Minimization for Tensor Completion with Arbitrary Sampling
For practitioners in video processing and tensor completion, ICNNM offers a faster and more accurate method than CNNM, though it is an incremental improvement over an existing approach.
The paper proposes Inductive Convolution Nuclear Norm Minimization (ICNNM) for tensor completion with arbitrary sampling, which reduces computational time by avoiding SVD and improves recovery performance over CNNM. Experiments show ICNNM achieves up to 2x speedup and better accuracy on video tasks.
The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary manner. Despite its promising performance, the optimization procedure of CNNM needs performing Singular Value Decomposition (SVD) multiple times, which is computationally expensive and hard to parallelize. To address the issue, we reformulate the optimization objective of CNNM from the perspective of convolution eigenvectors. By introducing pre-learned convolution eigenvectors which are shared among different tensors, we propose a novel method called Inductive Convolution Nuclear Norm Minimization (ICNNM), which bypasses the SVD step so as to decrease significantly the computational time. In addition, due to the extra prior knowledge encoded in the pre-learned convolution eigenvectors, ICNNM also outperforms CNNM in terms of recovery performance. Extensive experiments on video completion, prediction and frame interpolation verify the superiority of ICNNM over CNNM and several other competing methods.