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arXiv 2305.01166cs.LGeess.IVeess.SP
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利用含噪数据学习的基于分数的生成先验求解逆问题

Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data

Chandra Family Department of Electrical and Computer Engineering, The University of Texas at Austin(德克萨斯大学奥斯汀分校电气与计算机工程系);Intel Corporation(英特尔公司)

Asad Aali, Marius Arvinte, Sidharth Kumar, Jonathan I. Tamir

AI总结:

提出SURE-Score方法,利用含噪数据学习基于分数的生成先验,通过Stein无偏风险估计联合去噪与分数匹配,应用于压缩MIMO信道估计和加速MRI重建,在低信噪比下取得竞争性性能。

摘要:

我们提出SURE-Score:一种利用被加性高斯噪声污染的训练样本学习基于分数的生成模型的方法。当有大量干净样本的训练集可用时,基于分数的(扩散)生成模型在底层全采样数据分布上训练后用于求解逆问题,最近已被证明优于端到端的监督深度学习。然而在实践中,获取如此大量的训练数据可能首先就代价高昂。在本工作中,我们提出了一种从含噪训练数据中近似学习干净分布的基于分数的生成模型的方法。我们构建并论证了一个新颖的损失函数,该函数利用Stein无偏风险估计,通过去噪分数匹配联合进行数据去噪和分数函数学习,且仅使用含噪样本。我们通过在不同领域的两个实际应用中学习先验并对不适定逆问题应用后验采样,证明了SURE-Score的通用性:压缩无线多输入多输出信道估计和加速二维多线圈磁共振成像重建,我们分别展示了在信噪比为0 dB和10 dB下学习的竞争性重建性能。

英文摘要:

We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based (diffusion) generative models trained on the underlying fully-sampled data distribution has recently been shown to outperform end-to-end supervised deep learning. In practice, such a large collection of training data may be prohibitively expensive to acquire in the first place. In this work, we present an approach for approximately learning a score-based generative model of the clean distribution, from noisy training data. We formulate and justify a novel loss function that leverages Stein's unbiased risk estimate to jointly denoise the data and learn the score function via denoising score matching, while using only the noisy samples. We demonstrate the generality of SURE-Score by learning priors and applying posterior sampling to ill-posed inverse problems in two practical applications from different domains: compressive wireless multiple-input multiple-output channel estimation and accelerated 2D multi-coil magnetic resonance imaging reconstruction, where we demonstrate competitive reconstruction performance when learning at signal-to-noise ratio values of 0 and 10 dB, respectively.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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