Mixed-Noise Plug-and-Play with Infimal Convolution Fidelities and Multiple Priors
Abstract
Plug-and-Play (PnP) algorithms are a class of iterative methods for inverse imaging. Within an optimization algorithm, they combine a flexible fidelity term, encoding the forward operator, and a pretrained image denoiser, in order to deal with more severe corruptions such as blurring or downsampling when reconstructing an image. This work studies provably convergent PnP methods for mixed-noise forward processes by using the infimal convolution as a fidelity term, providing a statistical interpretation as a joint maximum a-posteriori estimator over both noises, and preserving the Bayesian MAP interpretation of PnP methods. Independently, we extend the PnP formulation to multiple prior terms using the Davis--Yin three-operator splitting. This extension can be combined with either standard fidelities or the proposed mixed-noise infimal-convolution fidelities. We verify that these generalized PnP methods are convergent under standard Kurdyka--Lojasiewicz conditions. Numerical experiments on Laplace-Gaussian and Poisson--Gaussian noise demonstrate stable convergence of single-prior and multiple-prior PnP methods, and divergence under fidelity mismatch. Furthermore, PnP with infimal convolution fidelities are able to scale to noise up to 38% standard deviation, with multiple priors reaching different stationary points that qualitatively preserve more textural properties.
Related
- Ellipsoid Separation in Data-Dependent Time via Infimal Displacement Vectors
- Weighted sum formulas for finite multiple mixed values
- Unramified Motivic Alternating Multiple Mixed Values
- Positive Bidiagonal Factorizations and Mixed-Type Chebyshev Multiple Orthogonal Polynomials
- Mixed sums of infinite multiple zeta-star values with restricted indices
BibTeX
@misc{qin2026mixednoise,
title = {{Mixed-Noise Plug-and-Play with Infimal Convolution Fidelities and Multiple Priors}},
author = {Ziqi Qin and Hong Ye Tan and Ander Biguri and Jingwei Liang and Carola-Bibiane Schönlieb},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33897},
eprint = {2609.33897},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33897},
}
RIS
TY - UNPB
TI - Mixed-Noise Plug-and-Play with Infimal Convolution Fidelities and Multiple Priors
AU - Ziqi Qin
AU - Hong Ye Tan
AU - Ander Biguri
AU - Jingwei Liang
AU - Carola-Bibiane Schönlieb
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33897
UR - https://arxiv.org/abs/2609.33897
AB - Plug-and-Play (PnP) algorithms are a class of iterative methods for inverse imaging. Within an optimization algorithm, they combine a flexible fidelity term, encoding the forward operator, and a pretrained image denoiser, in order to deal with more severe corruptions such as blurring or downsampling when reconstructing an image. This work studies provably convergent PnP methods for mixed-noise forward processes by using the infimal convolution as a fidelity term, providing a statistical interpretation as a joint maximum a-posteriori estimator over both noises, and preserving the Bayesian MAP interpretation of PnP methods. Independently, we extend the PnP formulation to multiple prior terms using the Davis--Yin three-operator splitting. This extension can be combined with either standard fidelities or the proposed mixed-noise infimal-convolution fidelities. We verify that these generalized PnP methods are convergent under standard Kurdyka--Lojasiewicz conditions. Numerical experiments on Laplace-Gaussian and Poisson--Gaussian noise demonstrate stable convergence of single-prior and multiple-prior PnP methods, and divergence under fidelity mismatch. Furthermore, PnP with infimal convolution fidelities are able to scale to noise up to 38% standard deviation, with multiple priors reaching different stationary points that qualitatively preserve more textural properties.
ER -