Year: 2026
Type: preprint
Abstract: Consider Gaussian denoising with a fixed prior and varying noise variance. When the prior has a density, maximum a posteriori estimation uses its negative logarithm as a fixed regularizer; only the weight of the quadratic data term changes with the noise variance. We ask whether a fixed regularizer can also recover the posterior mean. Although a suitable regularizer exists at each variance, we prove that no single regularizer works at two distinct positive variances for any compactly supported prior other than a point mass. This holds even for nonconvex and nonsmooth regularizers. A residual computed from two denoiser evaluations gives positive lower bounds on the uniform approximation error and excess mean squared error of estimators using a common regularizer. Numerical examples illustrate these bounds and the cost of reusing a regularizer across noise levels.
Source: arXiv (Cornell University)
Author: Liu, Kang
Institution: Xi'an Jiaotong University
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213232459