Image Compression Using Singular Value Decomposition

Image compression implementation using Singular Value Decomposition (SVD). The code provides compression algorithms for both grayscale and RGB true-color images.

In the SVD-based image compression method, image information can be efficiently compressed by performing singular value decomposition on the image matrix. Specifically, for grayscale images, the compression algorithm involves decomposing the image matrix into three components (U, S, V) using SVD, then reconstructing the image using only the top-k singular values to achieve compression. The key MATLAB functions used include svd() for decomposition and matrix multiplication for reconstruction.

Similarly, for RGB true-color images, the method applies SVD separately to each color channel (Red, Green, Blue). The implementation requires processing each channel matrix independently and then combining the compressed channels to reconstruct the color image. This approach significantly reduces image file size, conserving storage space and accelerating transmission speeds.

The compression ratio can be controlled by adjusting the number of retained singular values, balancing between compression efficiency and image quality. This SVD-based compression technique holds significant application value in digital image processing, particularly in scenarios requiring efficient storage and transmission of visual data.