Image compression is the process of reducing the file size of a digital image without significantly degrading the quality of the image. One approach to image compression is to use the singular value decomposition (SVD).

SVD is a mathematical technique that decomposes a matrix into three smaller matrices. When applied to an image, SVD can be used to identify and eliminate redundancies in the data, resulting in a compressed representation of the image that requires fewer bits to encode.

To use SVD for image compression, the image is first represented as a matrix of pixel values. The SVD is then applied to this matrix to decompose it into three smaller matrices: a left singular matrix, a diagonal matrix of singular values, and a right singular matrix. The singular values in the diagonal matrix represent the importance of each component of the original image matrix. By keeping only the most important singular values and discarding the rest, it is possible to significantly reduce the size of the matrix while still preserving much of the original image information. The compressed matrix can then be reconstructed using the retained singular values and the left and right singular matrices, resulting in a compressed version of the original image.