Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer
<|reference_start|>Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer: An image denoiser can be used for a wide range of restoration problems via the Plug-and-Play (PnP) architecture. In this paper, we propose a general framework to build an interpretable graph-based deep denoiser (GDD) by unrolling a solution to a maximum a posteriori (MAP) problem equipped with a graph Laplacian regularizer (GLR) as signal prior. Leveraging a recent theorem showing that any (pseudo-)linear denoiser $\boldsymbol \Psi$, under mild conditions, can be mapped to a solution of a MAP denoising problem regularized using GLR, we first initialize a graph Laplacian matrix $\mathbf L$ via truncated Taylor Series Expansion (TSE) of $\boldsymbol \Psi^{-1}$. Then, we compute the MAP linear system solution by unrolling iterations of the conjugate gradient (CG) algorithm into a sequence of neural layers as a feed-forward network -- one that is amenable to parameter tuning. The resulting GDD network is "graph-interpretable", low in parameter count, and easy to initialize thanks to $\mathbf L$ derived from a known well-performing denoiser $\boldsymbol \Psi$. Experimental results show that GDD achieves competitive image denoising performance compared to competitors, but employing far fewer parameters, and is more robust to covariate shift.<|reference_end|>
@article{hosseini2024constructing,
    title={Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian
  Regularizer},
    author={Seyed Alireza Hosseini, Tam Thuc Do, Gene Cheung, Yuichi Tanaka},
    journal={arXiv preprint arXiv:2409.06676},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.06676},
    primaryClass={eess.IV cs.CV eess.SP}
}