This paper presents a novel study of logarithmic discrete wavelet transform (DWT) for medical image compression. It proposes a new technique to compute the DWT using the logarithmic number system (LNS) instead of floating point arithmetic. It investigates its impact on the image quality which is an essential factor for medical images to avoid any misdiagnose. The paper presents detailed experimental results for three medical images modalities: CT, MRI and X-Ray. The results show that the LNS approach gives a significant improvement in the image quality measured with the structural similarity index (SSIM ).