Successful image denoising methods focus on preserving edges, which are crucial for maintaining the integrity of the image's features.

Neural networks often do not need to solve optimization problems exactly; instead, they minimize loss over a finite set of training examples, which is only an approximation of the larger problem.

While handcrafted models for image denoising are still relevant, deep neural networks are increasingly outperforming them in various scenarios.

The integration of handcrafted models with neural networks presents exciting opportunities for mathematicians to explore and improve image denoising techniques.

Denoising is integrated into the image reconstruction process, addressing both the lack of data and the noise present in measurements.

Total variation regularization is a widely used technique in image denoising that helps preserve sharp discontinuities in images.

Neural networks can struggle with images they haven't been trained on, highlighting the continued importance of handcrafted models in certain contexts.

To generalize well, you might not want to minimize the loss exactly over the training set, as this could lead to overfitting and poor performance on unseen data.

The success of deep learning in AI has been driven by the ability to train models on large datasets, such as ImageNet, which has led to significant improvements in image recognition tasks. In the past few years, the error rate in image recognition has dropped dramatically, with some teams achieving as low as 3% error, which is considered superhuman performance.