The importance of image compression is now essential during transmission or storage processes in various data applications, especially in medical and biometric systems. To perform the effectiveness of the compression process on images and evaluate degradation caused by this process, image quality assessment becomes an important tool in image services. We note that the objective criteria in image quality depend especially on the image type and image texture composition. The actual tendency is to find metrics making better qualification on errors in compressed images and correlate with the human visual system. This paper presents an investigation to examine and evaluate image compression degradation by the use of a new tendency concept of image quality assessment based on texture and edge analysis. To perform and practice this evaluation, we compress the medical and biometric images using second-generation wavelet compression algorithms and study the degradation of texture information in these images.