To ensure optimal clinical performance of digital mammography, it is necessary to obtain images with high spatial resolution and low noise, keeping radiation exposure as low as possible. These requirements directly affect the interpretation of radiologists. The quality of a digital image should be assessed using objective measurements. In general, these methods measure the similarity between a degraded image and an ideal image without degradation (ground-truth), used as a reference. These methods are called Full-Reference Image Quality Assessment (FR-IQA). However, for digital mammography, an image without degradation is not available in clinical practice; thus, an objective method to assess the quality of mammograms must be performed without reference. The purpose of this study is to present a Normalized Anisotropic Quality Index (NAQI), based on the Rényi entropy in the pseudo-Wigner domain, to assess mammography images in terms of spatial resolution and noise without any reference. The method was validated using synthetic images acquired through an anthropomorphic breast software phantom, and the clinical exposures on anthropomorphic breast physical phantoms and patient’s mammograms. The results reported by this noreference index follow the same behavior as other well-established full-reference metrics, e.g., the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM). Reductions of 50% on the radiation dose in phantom images were translated as a decrease of 4dB on the PSNR, 25% on the SSIM and 33% on the NAQI, evidencing that the proposed metric is sensitive to the noise resulted from dose reduction. The clinical results showed that images reduced to 53% and 30% of the standard radiation dose reported reductions of 15% and 25% on the NAQI, respectively. Thus, this index may be used in clinical practice as an image quality indicator to improve the quality assurance programs in mammography; hence, the proposed method reduces the subjectivity inter-observers in the reporting of image quality assessment.