We present a new image quality assessment algorithm based on the phase and magnitude of the 2-D discrete Fourier transform. The basic idea is to compare the phase and magnitude of the reference and distorted images to compute the quality score. However, it is well known that the human visual system's sensitivity to different frequency components is not the same. We accommodate this fact via a simple yet effective strategy of non-uniform binning of the frequency components. This process also leads to reduced space representation of the image thereby enabling the reduced-reference (RR) prospects of the proposed scheme. We employ linear regression to integrate the effects of the changes in phase and magnitude. In this way, the required weights are determined via proper training and hence more convincing and effective. Last, using the fact that phase usually conveys more information than magnitude, we use only the phase for RR quality assessment. This provides the crucial advantage of further reduction in the required amount of reference image information. The proposed method is, therefore, further scalable for RR scenarios. We report extensive experimental results using a total of nine publicly available databases: seven image (with a total of 3832 distorted images with diverse distortions) and two video databases (totally 228 distorted videos). These show that the proposed method is overall better than several of the existing full-reference algorithms and two RR algorithms. Additionally, there is a graceful degradation in prediction performance as the amount of reference image information is reduced thereby confirming its scalability prospects. To enable comparisons and future study, a Matlab implementation of the proposed algorithm is available at http://www.ntu.edu.sg/home/wslin/reduced_phase.rar.