# A numerical method I keep returning to

Date: 2026-08-13

Author: Zhenzhao Tu

Before the richness question, there was a more ordinary applied-math object: recover an image with missing pixels by solving an L1-regularized problem in the DCT domain. Compare a modeling language against a proximal gradient method you actually wrote down. Tune the regularizer until the reconstruction stops looking like a theory and starts looking like a photograph.

I keep returning to it because the shape is honest. There is a loss, a proximal map, a Lipschitz constant, and a picture that either comes back or does not. Neural-network theory is allowed to be stranger than that. It is not allowed to be vaguer than that.

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