Analyzing α-divergence in Gaussian Rate-Distortion-Perception Theory
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911173087068160 |
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| author | Sourla, Martha V. Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios |
| author_facet | Sourla, Martha V. Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios |
| contents | The problem of estimating the information rate distortion perception function (RDPF), which is a relevant information-theoretic quantity in goal-oriented lossy compression and semantic information reconstruction, is investigated here. Specifically, we study the RDPF tradeoff for Gaussian sources subject to a mean-squared error (MSE) distortion and a perception measure that belongs to the family of α divergences. Assuming a jointly Gaussian RDPF, which forms a convex optimization problem, we characterize an upper bound for which we find a parametric solution. We show that evaluating the optimal parameters of this parametric solution is equivalent to finding the roots of a reduced exponential polynomial of degree α. Additionally, we determine which disjoint sets contain each root, which enables us to evaluate them numerically using the well-known bisection method. Finally, we validate our analytical findings with numerical results and establish connections with existing results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analyzing α-divergence in Gaussian Rate-Distortion-Perception Theory Sourla, Martha V. Serra, Giuseppe Stavrou, Photios A. Kountouris, Marios Information Theory The problem of estimating the information rate distortion perception function (RDPF), which is a relevant information-theoretic quantity in goal-oriented lossy compression and semantic information reconstruction, is investigated here. Specifically, we study the RDPF tradeoff for Gaussian sources subject to a mean-squared error (MSE) distortion and a perception measure that belongs to the family of α divergences. Assuming a jointly Gaussian RDPF, which forms a convex optimization problem, we characterize an upper bound for which we find a parametric solution. We show that evaluating the optimal parameters of this parametric solution is equivalent to finding the roots of a reduced exponential polynomial of degree α. Additionally, we determine which disjoint sets contain each root, which enables us to evaluate them numerically using the well-known bisection method. Finally, we validate our analytical findings with numerical results and establish connections with existing results. |
| title | Analyzing α-divergence in Gaussian Rate-Distortion-Perception Theory |
| topic | Information Theory |
| url | https://arxiv.org/abs/2509.19572 |