arXiv subjects

Naeim Rezaeian

Publications and source records attributed to Naeim Rezaeian.

3 recordsLinked to original sources

arXiv2026

Efficient Techniques for Low-Rank Tensor Approximation and Applications in Robust Object Detection

This paper introduces efficient randomized fixed-precision and single-pass algorithms for low-tubal-rank approximation of third-order tensors. The proposed fixed-precision algorithms are faster and more efficient than the existing algorithms for approximating the truncated tensor SVD (T-SVD). Besides, unlike existing single-pass methods, which directly extend early, unstable matrix algorithms, the proposed approach adapts enhanced and stabilized matrix techniques to the tensor setting. Through extensive numerical experiments, we identify a critical flaw in current single-pass algorithms: using sketching parameters of equal size often produces ill-conditioned tensor least-squares problems, leading to inaccurate approximations. The proposed algorithms are demonstrably robust to this issue, achieving superior performance under identical conditions. We also evaluate the robustness of existing single-pass methods on real-world data tensors, including images and videos, a topic that has not been thoroughly examined before. Numerical results confirm the effectiveness of the proposed methods. Three applications are presented: image compression, video super-resolution, and deep learning.

math.NA↗

arXiv2026

Fast randomized Kronecker tensor decomposition: algorithms and error analysis

This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD) by replacing the sequence of deterministic SVDs in the TTr1SVD framework with randomized SVDs incorporating oversampling and power iterations. The proposed algorithms can decompose a given tensor into the KTD format significantly faster than existing state-of-the-art deterministic methods. Our principal idea is to use randomization to reduce computational complexity while maintaining controlled accuracy. A detailed theoretical analysis is presented, including a recursive error bound that accounts for error propagation through the TTr1SVD tree structure. We prove that the expected Frobenius norm error is bounded by a sum of tail energies multiplied by factors that decay exponentially with the number of power iterations. Extensive simulations on synthetic and real-world datasets demonstrate several orders of magnitude acceleration compared to the deterministic approach, with applications to tensor completion, video/image compression, image denoising, and image super-resolution.

math.NA↗

arXiv2026

A note on generalized tensor CUR approximation for tensor pairs and tensor triplets based on the tubal product

In this note, we briefly present a generalized tensor CUR (GTCUR) approximation for tensor pairs (X,Y) and tensor triplets (X,Y,Z) based on the tubal product (t-product). We use the tensor Discrete Empirical Interpolation Method (TDEIM) to do these extensions. We show how the TDEIM can be utilized to generalize the classical tensor CUR (TCUR) approximation, which acts only on a single tensor, to jointly compute the TCUR of two and three tensors. This approach can be used to sample relevant lateral/horizontal slices of one data tensor relative to one or two other data tensors. For some special cases, the Generalized TCUR (GTCUR) approximation is reduced to the classical TCUR for both tensor pairs and tensor triplets in a similar fashion as shown for the matrices.

math.NA↗