Provably Convergent Data-Driven Convex-Nonconvex Regularization

Jeremy Budd; Zakhar Shumaylov; Carola Bibiane Schonlieb; Subhadip Mukherjee

Provably Convergent Data-Driven Convex-Nonconvex Regularization

Jeremy Budd, Zakhar Shumaylov^*, Carola Bibiane Schonlieb, Subhadip Mukherjee

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how well-posedness and convergent regularisation arises within the convex-nonconvex (CNC) framework for inverse problems. We introduce a novel input weakly convex neural network (IWCNN) construction to adapt the method of learned adversarial regularization to the CNC framework. Empirically we show that our method overcomes numerical issues of previous adversarial methods.

Original language	English
Title of host publication	NeurIPS 2023 Workshop on Deep Learning and Inverse Problems
Number of pages	9
Publication status	Published - 23 Nov 2023

Keywords

Inverse problems
variational imaging
convergent regularisation
weak convexity
input-convex neural networks
data-driven regularization

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https://openreview.net/forum?id=yavtWi6ew9

Cite this

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title = "Provably Convergent Data-Driven Convex-Nonconvex Regularization",

abstract = "An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how well-posedness and convergent regularisation arises within the convex-nonconvex (CNC) framework for inverse problems. We introduce a novel input weakly convex neural network (IWCNN) construction to adapt the method of learned adversarial regularization to the CNC framework. Empirically we show that our method overcomes numerical issues of previous adversarial methods.",

keywords = "Inverse problems, variational imaging, convergent regularisation, weak convexity, input-convex neural networks, data-driven regularization",

author = "Jeremy Budd and Zakhar Shumaylov and Schonlieb, \{Carola Bibiane\} and Subhadip Mukherjee",

year = "2023",

month = nov,

day = "23",

language = "English",

booktitle = "NeurIPS 2023 Workshop on Deep Learning and Inverse Problems",

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TY - GEN

T1 - Provably Convergent Data-Driven Convex-Nonconvex Regularization

AU - Budd, Jeremy

AU - Shumaylov, Zakhar

AU - Schonlieb, Carola Bibiane

AU - Mukherjee, Subhadip

PY - 2023/11/23

Y1 - 2023/11/23

N2 - An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how well-posedness and convergent regularisation arises within the convex-nonconvex (CNC) framework for inverse problems. We introduce a novel input weakly convex neural network (IWCNN) construction to adapt the method of learned adversarial regularization to the CNC framework. Empirically we show that our method overcomes numerical issues of previous adversarial methods.

AB - An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of provable guarantees. In this work, we show how well-posedness and convergent regularisation arises within the convex-nonconvex (CNC) framework for inverse problems. We introduce a novel input weakly convex neural network (IWCNN) construction to adapt the method of learned adversarial regularization to the CNC framework. Empirically we show that our method overcomes numerical issues of previous adversarial methods.

KW - Inverse problems

KW - variational imaging

KW - convergent regularisation

KW - weak convexity

KW - input-convex neural networks

KW - data-driven regularization

M3 - Conference contribution

BT - NeurIPS 2023 Workshop on Deep Learning and Inverse Problems

ER -

Provably Convergent Data-Driven Convex-Nonconvex Regularization

Abstract

Keywords

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