The Blahut-Arimoto (BA) algorithm has played a fundamental role in the
numerical computation of rate-distortion (RD) functions. This algorithm
possesses a desirable monotonic convergence property by alternatively
minimizing its Lagrangian with a fixed multiplier. In this paper, we propose a
novel modification of the BA algorithm, letting the multiplier be updated in
each iteration via a one-dimensional root-finding step with respect to a
monotonic univariate function, which can be efficiently implemented by Newton's
method. This allows the multiplier to be updated in a flexible and efficient
manner, overcoming a major drawback of the original BA algorithm wherein the
multiplier is fixed throughout iterations. Consequently, the modified algorithm
is capable of directly computing the RD function for a given target distortion,
without exploring the entire RD curve as in the original BA algorithm. A
theoretical analysis shows that the modified algorithm still converges to the
RD function and the convergence rate is $\Theta(1/n)$, where $n$ denotes the
number of iterations. Numerical experiments demonstrate that the modified
algorithm directly computes the RD function with a given target distortion, and
it significantly accelerates the original BA algorithm.

通过使用一维根查找步骤和牛顿法更新固定乘数的 Blahut-Arimoto 算法的新修改版，可以使算法更加灵活和高效，直接计算给定目标失真下的速率失真函数，并且收敛速度为 O（1/n）。