Interpolative decomposition and its applications

Ng, Hao Tian (2024) Interpolative decomposition and its applications. Final Year Project, UTAR.

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Abstract

Matrix decomposition is extremely useful for data compression and efficient storage. As images are increasingly used across the Internet, the challenge of managing large file sizes becomes more significant. However, higher-qualityimages often come with large file sizes, making transmission extremely cumbersome. Matrix decomposition techniques can address this issue by compressing images to smaller file sizes while preserving much of the image fidelity. Although Singular Value Decomposition (SVD) has been widely used, Interpolative Decomposition (ID) has recently emerged as an alternative. This report explores the applicability of ID in image processing, particularly in image compression and compares its performance with that of SVD. We used four different images with unique characteristics to evaluate the performance of the matrix decomposition methods. Based on this, we deduced general compression parameters for both methods and tested these parameters using a separate image. All images were taken from the USC-SIPI Image Database. Our analysis showed that both ID and SVD struggled to compress images with darker regions. Nevertheless, ID generally produced better image quality, while SVD was more effective in reducing file size. For 512 × 512 pixel images, we established the following generalised compression parameters: for grayscale images,

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