Block-coordinate Plug-And-Play Methods with Armijo-like line-search for Image Restoration

Paper (arXiv)

Setup Environment

1. Create the conda environment

conda env create --file "environment.yml"

2. Activate the environment

conda activate blockPHILA

Run experiments

1. Replicate the experiment contained in the paper.

bash run_experiments.sh

2. Check the metrics.

tensorboard --logdir=results

The Block-PHILA variants

Each variant is identified by three independent design choices, recorded in its name as

Block-PHILA-<splitting>-<steplength>[-I][-VM]

tag	meaning
FB	forward-backward splitting: the proximal step acts on the data fidelity term
GD	all-smooth splitting: a gradient step is taken on the whole objective function
BB	adaptive Barzilai-Borwein steplength
C	constant steplength
I	FISTA-like inertial term (absent tag = no inertia)
VM	variable metric (absent tag = identity scaling matrix)

The eight configurations obtained by combining the splitting, the steplength rule and the inertial term are the following.

variant	splitting	steplength $\alpha_k$	inertia $\beta_k$	$N=1$ reduces to	legacy name
FB-BB-I	FB	Barzilai-Borwein	FISTA	PHILA	phila1
FB-BB	FB	Barzilai-Borwein	$0$	VMILA	phila2
FB-C-I	FB	constant	FISTA	PHILA	phila3
FB-C	FB	constant	$0$	VMILA	phila4
GD-BB-I	GD	Barzilai-Borwein	FISTA	full-gradient PHILA	phila5
GD-BB	GD	Barzilai-Borwein	$0$	full-gradient VMILA	phila6
GD-C-I	GD	constant	FISTA	full-gradient PHILA	phila7
GD-C	GD	constant	$0$	full-gradient VMILA	phila8

Citation

Please consider citing Block PHILA PnP if you find it helpful.

@article{porta2026block,
  title={Block-coordinate Plug-And-Play Methods with Armijo-like line-search for Image Restoration},
  author={Porta, Federica and Rebegoldi, Simone and Sebastiani, Andrea},
  journal={arXiv preprint arXiv:2603.01734},
  year={2026}
}