MATLAB Source Code for SVD Algorithm with BMP Image Compression Example

MATLAB source code implementation based on the Singular Value Decomposition (SVD) algorithm, using compression of .bmp format bitmap images as a practical example. The SVD algorithm is a widely-used image compression technique that performs matrix decomposition on bitmap data, enabling dimensionality reduction of image information to achieve file size compression. In this demonstration, we develop MATLAB code to read .bmp format bitmap files, perform SVD decomposition, and implement compression processing. The implementation includes using MATLAB's built-in svd() function for matrix factorization and strategic rank reduction to compress image data. We begin by explaining the mathematical principles and background of SVD algorithm, particularly focusing on how the decomposition A = UΣV^T allows for optimal low-rank approximations. Then we systematically demonstrate the MATLAB implementation process: reading bitmap files using imread(), converting color spaces if necessary, applying SVD to image matrices, selecting appropriate singular value thresholds, and reconstructing compressed images. The complete source code is provided with comprehensive comments, covering key aspects such as singular value thresholding strategies, compression ratio calculation, and image quality assessment using PSNR metrics. This enables readers to not only understand and execute the algorithm but also customize and optimize it for practical applications, including parameter adjustment for different compression requirements and image types.