In this paper, we study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources subject to a single-letter average distortion constraint and a perception constraint that belongs to the family of f-divergences. For that, we leverage the fact that RDPF, assuming mild regularity conditions on the perception constraint, forms a convex programming problem. We first develop parametric characterizations of the optimal solution and utilize them in an alternating minimization approach for which we prove convergence guarantees. The resulting structure of the iterations of the alternating minimization approach renders the implementation of a generalized Blahut-Arimoto (BA) type of algorithm infeasible. To overcome this difficulty, we propose a relaxed formulation of the structure of the iterations in the alternating minimization approach, which allows for the implementation of an approximate iterative scheme. This approximation is shown, via the derivation of necessary and sufficient conditions, to guarantee convergence to a globally optimal solution. We also provide sufficient conditions on the distortion and the perception constraints which guarantee that our algorithm converges exponentially fast. We corroborate our theoretical results with numerical simulations, and we draw connections with existing results.

翻译：本文研究离散无记忆信源在单字符平均失真约束及属于f-散度族的感知约束下的速率-失真-感知函数（RDPF）计算问题。为此，我们利用RDPF在感知约束满足温和正则性条件下构成凸优化问题的特性。首先建立最优解的参数化表征，并将其应用于交替最小化方法中，同时证明该方法的收敛性保证。交替最小化方法迭代结构的内在特性使得传统Blahut-Arimoto（BA）类算法的实现不可行。为克服这一困难，我们提出交替最小化方法迭代结构的松弛形式，从而允许近似迭代方案的实现。通过推导必要充分条件，证明该近似方案可保证收敛到全局最优解。我们还给出了确保算法指数级快速收敛的失真与感知约束的充分条件。通过数值仿真验证理论结果，并与现有研究成果建立关联。