Singular Value Decomposition (SVD) is adopted for image compression of the data matrix to obtain an optimal compression ratio and a clear compressed image. The principle of SVD and its application to compressing images are elaborated. Two methods for obtaining the better number of eigenvalues are proposed including the ratio threshold of eigenvalue number and the ratio threshold of eigenvalue sum. The experiments reveal that when the ratio threshold of eigenvalue number is 0.1, a clear image is obtained with the compression ratio of 5.99. When the ratio threshold of eigenvalue sum is 0.85, a clear image is also acquired with the compression ratio for PNG images of 7.89 and that for JPG images of 5.92. Case study indicates that the first 1% of eigenvalues represent more data characteristics. When the ratio threshold of eigenvalue number is determined, the compression ratios for PNG and JPG images are identical. When the ratio threshold of the eigenvalue sum is determined, the compression ratio for PNG images is higher than that for JPG images. The method for obtaining the eigenvalue number according to the ratio threshold of eigenvalue sum is more universal. It can be applied to solving alpha channel redundancy and setting a unified ratio threshold of eigenvalue sum for large-scale image compression.