Michaël Unser

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Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

Michaël Unser, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer

We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000) and offer a signal ...

2024

Linear inverse problems with Hessian-Schatten total variation

Michaël Unser, Shayan Aziznejad

In this paper, we characterize the class of extremal points of the unit ball of the Hessian-Schatten total variation (HTV) functional. The underlying motivation for our work stems from a general representer theorem that characterizes the solution set of re ...

Springer Heidelberg2024

From Nano to Macro An overview of the IEEE Bio Image and Signal Processing Technical Committee

Michaël Unser, Dimitri Nestor Alice Van De Ville, Michael Stefan Daniel Liebling

The Bio Image and Signal Processing (BISP) Technical Committee (TC) of the IEEE Signal Processing Society (SPS) promotes activities within the broad technical field of biomedical image and signal processing. Areas of interest include medical and biological ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Dynamic Fourier ptychography with deep spatiotemporal priors

Michaël Unser, Pakshal Narendra Bohra

Fourier ptychography (FP) involves the acquisition of several low-resolution intensity images of a sample under varying illumination angles. They are then combined into a high-resolution complex-valued image by solving a phase-retrieval problem. The object ...

IOP Publishing Ltd2023

Modulation Spaces and the Curse of Dimensionality

Michaël Unser, Rahul Parhi

2023

A Neural-Network-Based Convex Regularizer for Inverse Problems

Michaël Unser, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Stanislas Ducotterd

The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in quality. Unfortunately, these new methods often lack reliability and explainability, and there is a growing interest to address these ...

2023

The Sparsity of Cycle Spinning for Wavelet-Based Solutions of Linear Inverse Problems

Michaël Unser, Rahul Parhi

The usual explanation of the efficacy of wavelet-based methods hinges on the sparsity of many real-world objects in the wavelet domain. Yet, standard wavelet-shrinkage techniques for sparse reconstruction are not competitive in practice, one reason being t ...

IEEE Institute of Electrical and Electronics Engineers2023

Delaunay-Triangulation-Based Learning With Hessian Total-Variation Regularization

Michaël Unser, Alexis Marie Frederic Goujon, Mehrsa Pourya

2023

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems"

Michaël Unser, Pakshal Narendra Bohra, Alexis Marie Frederic Goujon, Sebastian Jonas Neumayer, Stanislas Ducotterd

Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems". The corresponding scripts can be accessed on GitHub (https://github.com/axgoujon/convex_ridge_regularizers). The data is organized as follows: - ct_data_sets.tar.gz: contains prepr ...

Zenodo2023

Phase Retrieval: From Computational Imaging to Machine Learning: A tutorial

Michaël Unser, Thanh-An Michel Pham, Jonathan Yuelin Dong

Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches involve techniqu ...

2023

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