The objective of this study was to develop a method for measuring quality degradation in lossy wavelet image compression. Quality degradation is due to denoising and edge blurring effects that cause smoothness in the compressed image. The peak Moran z histogram ratio between the reconstructed and original images is used as an index for degradation after image compression. The Moran test is applied to images randomly selected from each medical modality, computerized tomography, magnetic resonance imaging, and computed radiography and compressed using the wavelet compression at various levels. The relationship between the quality degradation and compression ratio for each image modality agrees with previous reports that showed a preference for mildly compressed images. Preliminary results show that the peak Moran z histogram ratio can be used to quantify the quality degradation in lossy image compression. The potential for this method is applications for determining the optimal compression ratio (the maximized compression without seriously degrading image quality) of an image for teleradiology.