BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Convex Regularizers Based on Shallow Neural Networks

S. Neumayer

Workshop on Mathematical Models for Plug-And-Play Image Restoration (WMMPAPIR'22), Paris, French Republic, December 7-8, 2022.

In this talk, we will revisit the state-of-the-art in learned convex regularisation. As comparison, we propose a regulariser based on a one hidden layer neural network with (almost) free-form activation functions. For training this network, we rely on some connection to gradient based denoisers. Our numerical experiments indicate that this shallow architecture already achieves the best performance, which is very different from the nonconvex case. Moreover, even when learning both the filters and the activation functions, we recover wavelet-like filters and thresholding-like activation functions. These observations raise the question if the fundamental limit is already reached in the convex setting. 

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