The paper proposes a general framework to construct an interpretable graph-based deep denoiser (GDD) in three main steps:
Select a trusted (pseudo-)linear denoiser Ψ with known good denoising performance, such as the bilateral filter (BF).
Approximate the corresponding graph Laplacian matrix L = μ^-1(Ψ^-1 - I_N) using truncated Taylor series expansion (TSE), leveraging a recent theorem that maps any (pseudo-)linear denoiser Ψ to an equivalent graph filter for a MAP denoising problem with GLR as prior.
Solve the linear system (I_N + μL)x^* = y to compute the denoised output x^* by unrolling the conjugate gradient (CG) algorithm into a feed-forward network (FFN), which is amenable to end-to-end parameter tuning.
The resulting GDD network is "graph-interpretable", low in parameter count, and easy to initialize thanks to L derived from a known well-performing denoiser Ψ. Experimental results show that GDD achieves competitive image denoising performance compared to competitors, while employing far fewer parameters, and is more robust to covariate shift.
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by Seyed Alirez... at arxiv.org 09-11-2024
https://arxiv.org/pdf/2409.06676.pdfDeeper Inquiries