Dr. Tsui-Wei Weng
Nov 28, 2023
DSC 210 FA’23 Numerical Linear Algebra
Dinesh Karthikeyan PID: A59026248 Halıcıoğlu Data Science Institute
Nandita Sanjivi PID: A69027955 Halıcıoğlu Data Science Institute
Prathish Murugan PID: A69027919 Halıcıoğlu Data Science Institute
Image Compression is the process of reducing the size of the image without significantly compromising its visual quality. This is essential for various applications, including storage, transmission and efficient utilization of resources.
In this project, we explore the conventional linear algebra-based approach as well as the state-of-the-art approach for image compression. The comparison of Singular Value Decomposition (SVD) with the SOTA approach of using High Fidelity Generative Compression is carried out in this study.
The SVD algorithm was discovered and developed independently by a number of mathematicians. Eugenio Beltrami and Camille Jordan were the first to do so, in 1873 and 1874, respectively; they were followed by James Joseph Sylvester, Erhard Schmidt, and Hermann Weyl, among others. The first proof for rectangular and complex matrices was given by Carl Eckart and Gale J. Young in 1936, and methods for computing the SVD of a matrix continued to be refined throughout the mid-20th century, revolutionizing the field of numerical linear algebra.
In the realms of mathematics, data science, and computer science/information technology, image compression is fundamentally rooted in sophisticated mathematical constructs and algorithms aimed at efficiently representing visual information. Mathematically, techniques like Singular Value Decomposition (SVD) and discrete wavelet transforms are employed to decompose images into components that capture essential information while discarding redundancies.
In data science, the utilization of compressed images accelerates the preprocessing and analysis phases, leveraging techniques like clustering and dimensionality reduction for effective pattern recognition and feature extraction.
SVD method can transform matrix A into product USV^T , which allows us to refactoring a digital image in three matrices. The using of singular values of such refactoring allows us to represent the image with a smaller set of values, which can preserve useful features of the original image, but use less storage space in the memory, and achieve the image compression process. The experiments with different singular value are performed, and the compression result was evaluated by compression ratio and quality measurement. [1]
In computer science and information technology, the intricacies lie in the design and implementation of compression algorithms such as the JPEG standard, where entropy coding and quantization are pivotal for achieving a balance between perceptual image quality and reduced file sizes. Moreover, advancements in lossless compression algorithms, like those used in medical imaging (e.g., DICOM), underscore the critical role of image compression in optimizing storage, transmission, and computational efficiency across diverse applications.