  Blind image deblurring (BID) has been extensively studied in computer vision
and adjacent fields. Modern methods for BID can be grouped into two categories:
single-instance methods that deal with individual instances using statistical
inference and numerical optimization, and data-driven methods that train
deep-learning models to deblur future instances directly. Data-driven methods
can be free from the difficulty in deriving accurate blur models, but are
fundamentally limited by the diversity and quality of the training data --
collecting sufficiently expressive and realistic training data is a standing
challenge. In this paper, we focus on single-instance methods that remain
competitive and indispensable. However, most such methods do not prescribe how
to deal with unknown kernel size and substantial noise, precluding practical
deployment. Indeed, we show that several state-of-the-art (SOTA)
single-instance methods are unstable when the kernel size is overspecified,
and/or the noise level is high. On the positive side, we propose a practical
BID method that is stable against both, the first of its kind. Our method
builds on the recent ideas of solving inverse problems by integrating the
physical models and structured deep neural networks, without extra training
data. We introduce several crucial modifications to achieve the desired
stability. Extensive empirical tests on standard synthetic datasets, as well as
real-world NTIRE2020 and RealBlur datasets, show the superior effectiveness and
practicality of our BID method compared to SOTA single-instance as well as
data-driven methods. The code of our method is available at:
\url{https://github.com/sun-umn/Blind-Image-Deblurring}.
