# Iterative Block Tensor Singular Value Thresholding for Extraction of Low Rank Component of Image Data

arXiv: https://arxiv.org/abs/1701.04043 · HTML: https://mlsanity.com/paper/1701.04043/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2017.

## Built on by (most cited first, 4 of 4)

- [Training Tensor Attention Efficiently: From Cubic to Almost Linear Time](https://mlsanity.com/paper/2405.16411/) (2024)
- [Theoretical Constraints on the Expressive Power of mathsfRoPE-based Tensor Attention Transformers](https://mlsanity.com/paper/2412.18040/) (2024)
- [Non-Convex Tensor Low-Rank Approximation for Infrared Small Target Detection](https://mlsanity.com/paper/2105.14974/) (2021)
- [Time and Memory Trade-off of KV-Cache Compression in Tensor Transformer Decoding](https://mlsanity.com/paper/2503.11108/) (2025)

## Abstract (arXiv)

Tensor principal component analysis (TPCA) is a multi-linear extension of principal component analysis which converts a set of correlated measurements into several principal components. In this paper, we propose a new robust TPCA method to extract the princi- pal components of the multi-way data based on tensor singular value decomposition. The tensor is split into a number of blocks of the same size. The low rank component of each block tensor is extracted using iterative tensor singular value thresholding method. The prin- cipal components of the multi-way data are the concatenation of all the low rank components of all the block tensors. We give the block tensor incoherence conditions to guarantee the successful decom- position. This factorization has similar optimality properties to that of low rank matrix derived from singular value decomposition. Ex- perimentally, we demonstrate its effectiveness in two applications, including motion separation for surveillance videos and illumination normalization for face images.