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

Parseval Convolution Neural Networks with Application to Imaging

M. Unser

Summer School on Applied Harmonic Analysis and Machine Learning 2024 (AHAML'24), Genova, Italian Republic, September 2-6, 2024.

One of the reasons why neural networks can occasionally hallucinate is their lack stability. Our proposed remedy is to constrain the Lipschitz constant of each layer to be non-expansive; i.e., with a Lipschitz constant no greater than 1. We can further constrain the linear layers to be energy-preserving. This motivates us to thoroughly characterize the class of Parseval convolution operators. We then present a constructive approach for the design/specification of such filterbanks via the chaining of elementary Parseval modules, each parameterized by an orthogonal matrix or a 1-tight frame. We demonstrate the usage of those tools with the design of a CNN-based algorithm for the iterative reconstruction of biomedical images. Our algorithm falls within the plug-and-play framework for the resolution of inverse problems. It yields better-quality results than the sparsity-based methods used in compressed sensing, while offering essentially the same convergence and robustness guarantees. 

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AUTHOR="Unser, M.",
TITLE="Parseval Convolution Neural Networks with Application to
	Imaging",
BOOKTITLE="Summer School on Applied Harmonic Analysis and Machine
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YEAR="2024",
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address="Genova, Italian Republic",
month="September 2-6,",
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