tenSVD algorithm for compression
Michele Gallo
TL;DR
The paper tackles efficient compression of high-dimensional image data using tensor methods, introducing tenSVD to reduce storage, bandwidth, and energy use while maintaining quality. TenSVD reshapes an Nth-order tensor into an M-order tensor, applies HOSVD on the rearranged tensor, and selectively retains high-energy core elements along with the corresponding factor matrices. Empirical results on images and a video show tenSVD achieves comparable PSNR/MSE/ERR to HOSVD at fixed CR but with substantial speedups (up to ~27× in some cases, and ~2.5× for video), highlighting improved energy efficiency. The work discusses trade-offs, including scenarios where tenSVD may not recover true latent structure, and positions it as a practical, faster alternative for energy-conscious tensor-based compression in imaging applications.
Abstract
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis, and data mining. This study introduces an efficient image storage approach utilizing tensors, aiming to minimize memory to store, bandwidth to transmit and energy to processing. The proposed method organizes original data into a higher-order tensor and applies the Tucker model for compression. Implemented in R, this method is compared to a baseline algorithm. The evaluation focuses on efficient of algorithm measured in term of computational time and the quality of information preserved, using both simulated and real datasets. A detailed analysis of the results is conducted, employing established quantitative metrics, with significant attention paid to sustainability in terms of energy consumption across algorithms.