[論文レビュー] Invertible generative models for inverse problems: mitigating representation error and dataset bias

Muhammad Asim, Max Daniels+3 more|arXiv (Cornell University)|May 28, 2019

Generative Adversarial Networks and Image Synthesis参考文献 28被引用数 42

ひとこと要約

本論文は、事前学習済みの可逆ニューラルネットワーク（Glowベースの priors）が画像再構成問題におけるゼロ表現誤差プリオリとして機能し、ノイズ除去と圧縮感知においてGANベースのプリオリよりも優れていると示す。分布外データに対しても頑健で、データセットバイアスを緩和する。

ABSTRACT

Trained generative models have shown remarkable performance as priors for inverse problems in imaging -- for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training dataset. In this paper, we demonstrate that invertible neural networks, which have zero representation error by design, can be effective natural signal priors at inverse problems such as denoising, compressive sensing, and inpainting. Given a trained generative model, we study the empirical risk formulation of the desired inverse problem under a regularization that promotes high likelihood images, either directly by penalization or algorithmically by initialization. For compressive sensing, invertible priors can yield higher accuracy than sparsity priors across almost all undersampling ratios, and due to their lack of representation error, invertible priors can yield better reconstructions than GAN priors for images that have rare features of variation within the biased training set, including out-of-distribution natural images. We additionally compare performance for compressive sensing to unlearned methods, such as the deep decoder, and we establish theoretical bounds on expected recovery error in the case of a linear invertible model.

研究の動機と目的

• Invertible generative models can serve as natural priors for imaging inverse problems.
• Evaluate performance of invertible priors across denoising, compressive sensing, and inpainting.
• Compare invertible priors with GAN-based and unlearned priors under in-distribution and out-of-distribution settings.
• Provide theoretical bounds on recovery error for linear invertible generators.

提案手法

• Use a pretrained Glow invertible neural network as a signal prior for inverse problems.
• Formulate reconstruction as latent-space optimization with a likelihood proxy via latent norm, using z initialization at zero.
• Solve denoising with a regularized latent objective (minimizing data fit plus gamma times ||z||^2).
• Solve compressive sensing with an unconstrained latent objective (minimize data fit; gamma set to 0); initialize at z0=0.
• Compare against DCGAN, PGGAN, and Deep Decoder priors, and against Lasso-DCT baselines.
• Provide theoretical bounds for linear invertible generators on recovery error as a function of singular values.]
• research_questions: ["Can invertible priors provide zero representation error and thus recover any image, including out-of-distribution images, in inverse problems?", "How do invertible priors perform in denoising, compressive sensing, and inpainting compared to GAN-based priors across in-distribution and out-of-distribution data?", "What are the theoretical recovery-error bounds when the generator is linear under compressive sensing with Gaussian measurements?"]
• key_findings:["Invertible priors yield sharper denoised images and can outperform BM3D in PSNR under appropriate regularization.", "For in-distribution compressive sensing, Glow priors outperform low-dimensional GAN priors, Deep Decoder, and sparsity across a wide range of undersampling ratios.", "Glow priors show graceful performance degradation for out-of-distribution images and can outperform GANs with low latent dimensionality under many undersampling regimes.", "In extreme undersampling, Glow still substantially outperforms competing priors even without explicit low-dimensional manifold constraints.", "A theoretical bound shows the expected recovery error lies between the sum of squares of the smallest singular values and a multiple of that sum, clarifying why invertible priors can approach optimal recovery with enough measurements."]
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実験結果

リサーチクエスチョン

• RQ1 Can invertible priors provide zero representation error and thus recover any image, including out-of-distribution images, in inverse problems?

主な発見

• Invertible priors yield sharper denoised images and can outperform BM3D in PSNR under appropriate regularization.
• For in-distribution compressive sensing, Glow priors outperform low-dimensional GAN priors, Deep Decoder, and sparsity across a wide range of undersampling ratios.
• Glow priors show graceful performance degradation for out-of-distribution images and can outperform GANs with low latent dimensionality under many undersampling regimes.
• In extreme undersampling, Glow still substantially outperforms competing priors even without explicit low-dimensional manifold constraints.
• A theoretical bound shows the expected recovery error lies between the sum of squares of the smallest singular values and a multiple of that sum, clarifying why invertible priors can approach optimal recovery with enough measurements.