The important objective of image compression is reducing the quantity of data required by the applying an image encoding. This reduction is needed for transmission or database storage. Our used is based on the Wavelet transform in image compression. It offers ascend to numerous applications in different fields, for example, geophysics, astronomy, media communications, imaging, and video coding. This contribution presents an application in the compression of the biometric image based on the second-generation wavelet with lifting and combined with SPIHT progressive encoder. To study the reliability and performance of these algorithms, we apply them on iris image and use the image quality assessment with full reference (PSNR, MSSIM, VIF) and without reference (NIQE, BLIINDS). The obtained results are very interestingly and encouraging.