Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914946650996736 |
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| author | Hosseini, Seyed Alireza Do, Tam Thuc Cheung, Gene Tanaka, Yuichi |
| author_facet | Hosseini, Seyed Alireza Do, Tam Thuc Cheung, Gene Tanaka, Yuichi |
| contents | 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 $\boldsymbol Ψ$, 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 $\boldsymbol Ψ^{-1}$. 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 $\boldsymbol Ψ$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06676 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer Hosseini, Seyed Alireza Do, Tam Thuc Cheung, Gene Tanaka, Yuichi Image and Video Processing Computer Vision and Pattern Recognition Signal Processing 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 $\boldsymbol Ψ$, 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 $\boldsymbol Ψ^{-1}$. 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 $\boldsymbol Ψ$. 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. |
| title | Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer |
| topic | Image and Video Processing Computer Vision and Pattern Recognition Signal Processing |
| url | https://arxiv.org/abs/2409.06676 |