Image Compression using Singular Value Decomposition (SVD)

Abstract

Abstract Images, integral to numerous applications, are encoded as matrices where each element represents a pixel's grayscale intensity. In grayscale images, values range from 0 (representing black) to 1 (indicating white). As image dimensions increase, so does the demand for storage space. Smaller images are easily managed, but larger ones pose challenges. Hence, data compression techniques are applied to mitigate storage consumption. One effective approach involves employing Singular Value Decomposition (SVD) on the image matrix. Through SVD, we create a low-rank approximation for each color channel separately, resulting in a 3-dimensional array that closely approximates the original image. This process achieves image compression while retaining vital image characteristics. This paper illustrates the fundamental concept of SVD and demonstrates its remarkable efficacy in substantially reducing image storage requirements while preserving image quality to a nearly perfect degree. As an illustrative example, we utilized a grayscale image of a bird to showcase how SVD can generate a near-replica of the original image while utilizing only 7.82% of the original image's storage capacity. This underscores the practical importance of SVD in optimizing image storage and transmission.