Efficient Multi-Dimensional Tensor Sparse Coding Using t-Linear Combination
Year: 2018
Type: conference-paper
Abstract: In this paper, we propose two novel multi-dimensional tensor sparse coding (MDTSC) schemes using the t-linear combination. Based on the t-linear combination, the shifted versions of the bases are used for the data approximation, but without need to store them. Therefore, the dictionaries of the proposed schemes are more concise and the coefficients have richer physical explanations. Moreover, we propose an efficient alternating minimization algorithm, including the tensor coefficient learning and the tensor dictionary learning, to solve the proposed problems. For the tensor coefficient learning, we design a tensor-based fast iterative shrinkage algorithm. For the tensor dictionary learning, we first divide the problem into several nearly-independent subproblems in the frequency domain, and then utilize the Lagrange dual to further reduce the number of optimization variables. Experimental results on multi-dimensional signals denoising and reconstruction (3DTSC, 4DTSC, 5DTSC) show that the proposed algorithms are more efficient and outperform the state-of-the-art tensor-based sparse coding models.
Authors: Fei Jiang, Xiao-Yang Liu, Hongtao Lu, Ruimin Shen
Institutions: Shanghai Jiao Tong University, Columbia University
Language: English
Subfield: Computational Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: 深度神经网络压缩及其应用研究, G8562762075
OpenAlex ID: W2788913644