  Digital image compression is a technique that allows to reduce the size of an
image in order to increase the capacity storage devices and to optimize the use
of network bandwidth. The quality of compressed images with the techniques
based on the discrete cosine transform or the wavelet transform is generally
measured with PSNR or SSIM. Theses metrics are not suitable to images
compressed with the singular values decomposition. This paper presents a new
metric based on the energy ratio to measure the quality of the images coded
with the SVD. A series of tests on 512 * 512 pixels images show that, for a
rank k = 40 corresponding to a SSIM = 0,94 or PSNR = 35 dB, 99,9% of the energy
are restored. Three areas of image quality assessments were identified. This
new metric is also very accurate and could overcome the weaknesses of PSNR and
SSIM.
