---

In this paper, by considering the generalized chi-squared information and the relative generalized chi-squared information measures, discrete versions of these information measures are introduced. Then, generalizations of these information quantities based on their convexity property are presented. Some essential features of these new measures and their relationships are studied. Moreover, the performance of these new information measures is investigated for some well-known and widely used models in coding theory and thermodynamics, such as escort distributions and generalized escort distributions. Finally, two applications of the introduced discrete generalized chi-squared information measure are examined in the context of image quality assessment. In addition, the results obtained from the performance of these measures are compared with the performance of the critical metric, peak signal-to-noise ratio. It is shown that the generalized chi-squared divergence measure exhibits performance similar to the peak signal-to-noise ratio and can be used as an alternative metric.