Tensor LISTA: Differentiable sparse representation learning for multi-dimensional tensor

Qi Zhao, Guangcan Liu, Qingshan Liu

Abstract: The existing algorithms for sparse coding, which aim to seek sparse representation for given multi-dimensional signal, suffer from two main defects. Vector-based algorithms, e.g., LISTA, couldn’t handle the signal in tensor form well. On the other hand, tensor-based algorithms are not learnable yet, leading to high computational cost. Towards this dilemma, we propose Tensor LISTA (TLISTA) bA to a multi-dimensional tensor-based model. Benefiting from tensor representation and differentiable programming, TLISTA achieves rapid inference speed and acquires more valuable representation for the data primarily organized in tensor form. Theoretical analysis about the convergence of TLISTA is then introduced, showing that TLISTA can attain the linear convergence rate. Extensive experiments confirm the effectiveness and efficiency of TLISTA for tensor sparse coding.