Fundamental Principles and Characteristics of Singular Value Decomposition

In the following content, I will detail the fundamental principles and characteristics of Singular Value Decomposition (SVD) and present a method for image compression using SVD. First, I will illustrate the basic process and specific steps of the compression workflow through simple examples. The implementation typically involves decomposing the image matrix using MATLAB's svd() function, which returns three matrices: U, S, and V. The compression is achieved by retaining only the top k singular values from the diagonal matrix S, effectively reducing storage requirements while preserving essential image features. Next, I will demonstrate the method's effectiveness by processing actual images through MATLAB programming, including code segments for loading images with imread(), performing SVD, truncating singular values, and reconstructing compressed images using matrix multiplication. Through these detailed explanations and practical implementations, you will gain a deeper understanding of SVD's application in image compression.