We consider a denoiser that reconstructs a stationary ergodic source by lossily compressing samples of the source observed through a memoryless noisy channel. Prior work on compression-based denoising has been limited to additive noise channels. We extend this framework to general discrete memoryless channels by deliberately choosing the distortion measure for the lossy compressor to match the channel conditional distribution. By bounding the deviation of the empirical joint distribution of the source, observation, and denoiser outputs from satisfying a Markov property, we give an exact characterization of the loss achieved by such a denoiser. Consequences of these results are explicitly demonstrated in special cases, including for MSE and Hamming loss. A comparison is made to an indirect rate-distortion perspective on the problem.

翻译：本文研究一种去噪器，该去噪器通过对经过无记忆噪声信道观测到的平稳遍历源样本进行有损压缩，实现对源信号的重建。此前基于压缩的去噪研究仅限于加性噪声信道。我们通过为有损压缩器选择与信道条件分布相匹配的失真度量，将该框架推广至一般离散无记忆信道。通过约束源信号、观测值及去噪器输出的经验联合分布偏离马尔可夫性质的偏差，我们精确刻画了此类去噪器所达到的损失。这些结果在均方误差与汉明损失等特例中的具体表现被明确展示，并与该问题的间接率失真视角进行了比较。