Image quality assessment using the singular value decomposition theorem

In objective image quality metrics, one of the most important factors is the correlation of their results with the perceived quality measurements. In this paper, a new method is presented based on comparing between the structural properties of the two compared images. Based on the mathematical concept of the singular value decomposition (SVD) theorem, each matrix can be factorized to the products of three matrices, one of them related to the luminance value while the two others show the structural content information of the image. A new method to quantify the quality of images is proposed based on the projected coefficients and the left singular vector matrix of the disturbed image based on the right singular vector matrix of the original image. To evaluate this performance, many tests have been done using a widespread subjective study involving 779 images of the Live Image Quality Assessment Database, Release 2005. The objective results show a high rate of correlation with subjective quality measurements.