Reproduce “Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser” on OpenResearch

About this paper

Zahra Kadkhodaie, Eero P. Simoncelli

Researchers at NYU developed a method to solve various linear inverse problems by utilizing the implicit prior knowledge embedded within a single, pre-trained deep neural network denoiser, employing a stochastic coarse-to-fine gradient ascent that directly relates denoising to the gradient of a noisy signal's log-density. The approach demonstrates competitive reconstruction quality, often yielding perceptually superior results and significantly faster execution times than alternative unsupervised methods.

Key insights

• A high-performing least-squares denoiser implicitly computes the gradient of the log-probability density of noisy natural images, allowing its embedded prior to be directly accessed.
• A single, generic deep denoiser can serve as a universal prior for diverse linear inverse problems without needing additional task-specific training or fine-tuning, enabling efficient transfer learning.
• The stochastic optimization process can generate multiple, diverse, and perceptually plausible solutions for highly ill-posed inverse problems by sampling from the conditional implicit prior.

Summary by alphaXiv.