The impact of the entropy parameter in generalized information measures for image quality assessment

Abstract

We introduce and study Mathai’s cumulative residual entropy, a generalized entropy measure motivated by Mathai’s entropy. We establish fundamental properties, including finiteness, limiting behavior, and connections with existing cumulative residual entropy measures. The entropy parameter q is highlighted as a flexible mechanism for controlling sensitivity to distributional and structural features. The practical applicability of the proposed measure is illustrated through texture analysis and image quality assessment framework. Experimental results show that the entropy parameter q effectively captures variations in image degradation and structural characteristics. These findings show that the proposed Mathai’s cumulative residual entropy measure, compared with its Tsallis counterpart, provides a flexible and interpretable approach to texture analysis and blind image quality assessment.

Keywords

• Cumulative residual entropy
• generalized entropy
• image quality assessment
• information measures
• Tsallis entropy
• Mathai’s entropy.

References

1. [1] C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J., 27 (3), 379–423, 1948.
2. [2] C. Tsallis, Possible generalization of Boltzmann–Gibbs statistics, J. Stat. Phys., 52 (1), 479–487, 1988.
3. [3] A. M. Mathai and H. J. Haubold, Pathway model, Tsallis statistics, superstatistics, and a generalized measure of entropy, Phys. A: Stat. Mech. Appl., 375 (1), 110–122, 2007.
4. [4] M. Rao, Y. Chen, B. C. Vemuri, and F. Wang, Cumulative residual entropy: a new measure of information, IEEE Trans. Inf. Theory, 50 (6), 1220–1228, 2004.
5. [5] A. Di Crescenzo and M. Longobardi, On cumulative entropies, J. Stat. Plan. Inference, 139 (12), 4072–4087, 2009.
6. [6] A. M. Mathai, A pathway to matrix-variate gamma and normal densities, Linear Algebra Appl., 396, 317–328, 2005.
7. [7] A. M. Mathai and H. J. Haubold, Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy, Phys. A: Stat. Mech. Appl.,375 (1), 110–122, 2007.
8. [8] A. Di Crescenzo and M. Longobardi, On weighted residual and past entropies, Sci. Math. Jpn., 64 (2), 255–266, 2006.

9. [9] A. M. Mathai and P. N. Rathie, Basic concepts in information theory and statistics: axiomatic foundations and applications, Wiley Halsted, New York, and Wiley Eastern, New Delhi, 1975.
10. [10] T. Princy and S. Babu, A bivariate exponential distribution with q-exponential marginals and its applications, Stat. Optim. Inf. Comput., 15 (3), 2179–2195, 2026.
11. [11] N. Ebrahimi, How to measure uncertainty in the residual lifetime distribution, Sankhya Ser. A, 58 (1), 48–56, 1996.
12. [12] M. Asadi and Y. Zohrevand, On the dynamic cumulative residual entropy, J. Stat. Plan. Inference, 137 (6), 1931–1941, 2007.
13. [13] A. Toomaj and H. A. Atabay, Some new findings on the cumulative residual Tsallis entropy, J. Comput. Appl. Math., 400, 113669, 2022.
14. [14] A. Rényi, On measures of entropy and information, Proc. Fourth Berkeley Symp. Math. Stat. Probab., 1, 547–561, 1961.
15. [15] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Trans. Image Process., 13 (4), 600–612, 2004.
16. [16] H. R. Sheikh and A. C. Bovik, Image information and visual quality, IEEE Trans. Image Process., 15 (2), 430–444, 2006.
17. [17] Y. Cui, No-reference image quality assessment based on dual-domain feature fusion, Entropy, 22 (3), 344, 2020.
18. [18] S. Gabarda and G. Cristóbal, Blind image quality assessment through anisotropy, J. Opt. Soc. Am. A, 24 (12), B42–B51, 2007.
19. [19] A. M. Rohaly, P. J. Corriveau, J. M. Libert, A. A.Webster, V. Baroncini, J. Beerends, J. L. Blin, L. Contin, T. Hamada, D. Harrison and A. P. Hekstra, Video Quality Experts Group: Current results and future directions, Proc. SPIE Vis. Commun. Image Process., 4067, 742–753, 2000.