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Prior probability models are a fundamental component of many image processingproblems, but density estimation is notoriously difficult for high-dimensionalsignals such as photographic images. Deep neural networks have providedstate-of-the-art solutions for problems such as denoising, which implicitlyrely on a prior probability model of natural images. Here, we develop a robustand general methodology for making use of this implicit prior. We rely on astatistical result due to Miyasawa (1961), who showed that the least-squaressolution for removing additive Gaussian noise can be written directly in termsof the gradient of the log of the noisy signal density. We use this fact todevelop a stochastic coarse-to-fine gradient ascent procedure for drawinghigh-probability samples from the implicit prior embedded within a CNN trainedto perform blind (i.e., with unknown noise level) least-squares denoising. Ageneralization of this algorithm to constrained sampling provides a method forusing the implicit prior to solve any linear inverse problem, with noadditional training. We demonstrate this general form of transfer learning inmultiple applications, using the same algorithm to produce state-of-the-artlevels of unsupervised performance for deblurring, super-resolution,inpainting, and compressive sensing.

Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser