SVD Image Processing Implementation Using MATLAB

This program implements Singular Value Decomposition (SVD) for image processing using MATLAB. SVD is a fundamental matrix factorization method that decomposes any matrix into three component matrices: U, S, and V. The implementation typically involves converting the input image to a grayscale matrix and applying MATLAB's built-in svd() function to extract singular values and orthogonal matrices. Through SVD decomposition, we can extract the principal features of an image represented by the singular values in the S matrix. The algorithm allows for efficient image processing operations including compression by retaining only the most significant singular values, noise reduction by truncating smaller values, and image reconstruction by multiplying the reduced matrices. The program demonstrates how to control reconstruction quality by adjusting the number of preserved singular values using threshold parameters. This implementation helps users better understand and apply SVD in practical image processing scenarios, improving processing efficiency and output quality. Key MATLAB functions utilized include imread() for image loading, rgb2gray() for conversion, svd() for decomposition, and matrix multiplication operations for reconstruction. The code provides practical insights into optimizing the trade-off between compression ratio and image quality through singular value thresholding.