Deep image prior (DIP) and its variants have showed remarkable potential for solving inverse problems in computer vision, without any extra training data. Practical DIP models are often substantially overparameterized. During the fitting process, these models learn mostly the desired visual content first, and then pick up the potential modeling and observational noise, i.e., overfitting. Thus, the practicality of DIP often depends critically on good early stopping (ES) that captures the transition period. In this regard, the majority of DIP works for vision tasks only demonstrates the potential of the models-reporting the peak performance against the ground truth, but provides no clue about how to operationally obtain near-peak performance without access to the groundtruth. In this paper, we set to break this practicality barrier of DIP, and propose an efficient ES strategy, which consistently detects near-peak performance across several vision tasks and DIP variants. Based on a simple measure of dispersion of consecutive DIP reconstructions, our ES method not only outpaces the existing ones-which only work in very narrow domains, but also remains effective when combined with a number of methods that try to mitigate the overfitting. The code is available at https://github.com/sunumn/Early_Stopping_for_DIP.

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Recent works have shown the surprising effectiveness of deep generative models in solving numerous image reconstruction (IR) tasks, even without training data. We call these models, such as deep image prior and deep decoder, collectively as single-instance deep generative priors (SIDGPs). The successes, however, often hinge on appropriate early stopping (ES), which by far has largely been handled in an ad-hoc manner. In this paper, we propose the first principled method for ES when applying SIDGPs to IR, taking advantage of the typical bell trend of the reconstruction quality. In particular, our method is based on collaborative training and self-validation: the primal reconstruction process is monitored by a deep autoencoder, which is trained online with the historic reconstructed images and used to validate the reconstruction quality constantly. Experimentally, on several IR problems and different SIDGPs, our self-validation method is able to reliably detect near-peak performance and signal good ES points. Our code is available at https://sun-umn.github.io/Self-Validation/. IntroductionValidation-based ES is one of the most reliable strategies for controlling generalization errors in supervised learning, especially with potentially overspecified models such as in gradient boosting and modern DNNs [10,28,47]. Beyond supervised learning, ES often remains critical to learning success, but there are no principled ways-universal as validation for supervised learning-to decide when to stop. In this paper, we make the first step toward filling in the gap, and focus on solving IR, a central family of inverse problems, using training-free deep generative models.

The Qinshui Basin in Shanxi Province in northern China is currently the largest production area of coal bed methane (CBM) in China. For this study, methane (CH 4) measurements were collected from 113 wellheads to determine primary gas leakage locations. The results indicate that the leakage is primarily from water outlets and tubing; three leakage points accounted for 95.79% of the total measured gas. With respect to measurement variability, the standard deviation for gas measurements of the tubing was the largest at 12.28. Wells with good geological conditions and scientifi c management exhibited very low leakage. In contrast, wells with unfavorable geological conditions and improper management had much higher leakage values. The standard deviation of leakage at the water outlets was the next lowest. The role of different processes and running states had the greatest role in CH 4 leakage. The leakage from horizontal wellheads was the highest, with an average rate of 20.80 l/min, compared to the average of leakage from fl owing wells at 0.88 l/min; this is far below that of the wells that used mechanical gas pumping. T he overall emission factor of the 113 examined wells was 176 kg CO 2-e t-1 , which was far greater than the previously reported Australian emission level (11.7 kg CO 2-e t-1).

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