Functional learning: From theory to application in bioimaging

Publications

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions

Author(s): Ducotterd, Stanislas; Goujon, Alexis; Bohra, Pakshal; Perdios, Dimitris; Neumayer, Sebastian; Unser, Michael
Published in: Journal of Machine Learning Research, Issue 9, 2024, Page(s) 1-30, ISSN 1533-7928
Publisher: Microtome Publishing

Linear Inverse Problems with Hessian-Schatten Total Variation

Author(s): Ambrosio, Luigi; Aziznejad, Shayan; Brena, Camillo; Unser, Michael
Published in: Calculus of Variations and Partial Differential Equations, Issue vol. 63, no. 1, 2024, Page(s) paper no. 9, ISSN 1432-0835
Publisher: Springer
DOI: 10.1007/s00526-023-02611-6

Learning of Continuous and Piecewise-Linear Functions With Hessian Total-Variation Regularization

Author(s): Michael Unser; Shayan Aziznejad; Joaquim Campos
Published in: IEEE Open Journal of Signal Processing, Issue 3, 2022, Page(s) 36-48, ISSN 2644-1322
Publisher: IEEE
DOI: 10.1109/ojsp.2021.3136488

Explicit Representations for Banach Subspaces of Lizorkin Distributions

Author(s): Neumayer, Sebastian; Unser, Michael
Published in: Analysis and Applications, Issue vol. 21, no. 5, 2023, Page(s) 1223-1250, ISSN 1793-6861
Publisher: World Scientific Publishing Company
DOI: 10.1142/s0219530523500148

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

Author(s): Goujon, Alexis; Neumayer, Sebastian; Unser, Michael
Published in: Crossref, Issue 3, 2024, Page(s) 91-115, ISSN 1936-4954
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1565243

Artifacts in Optical Projection Tomography Due to Refractive-Index Mismatch: Model and Correction

Author(s): Liu, Yan; Dong, Jonathan; Schmidt Cédric; Boquet-Pujada, Aleix; Extermann, Jérôme; Unser, Michael
Published in: Optics Letters, Issue 47(11), 2022, Page(s) 2618-2621, ISSN 0146-9592
Publisher: Optical Society of America
DOI: 10.1364/ol.457144

Deep Learning Meets Sparse Regularization: A signal processing perspective

Author(s): Rahul Parhi; Robert D. Nowak
Published in: Crossref, Issue 10, 2023, Page(s) 63-74, ISSN 1558-0792
Publisher: IEEE
DOI: 10.1109/msp.2023.3286988

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

Author(s): Dong, Jonathan; Valzania, Lorenzo; Maillard, Antoine; Pham, Thanh-an; Gigan, Sylvain; Unser, Michael
Published in: IEEE Signal Processing Magazine, Issue vol. 40, no. 1, 2023, Page(s) pp. 45–57, ISSN 1053-5888
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/msp.2022.3219240

Learning of Continuous and Piecewise-Linear Functions with Hessian Total-Variation Regularization

Author(s): Campos, Joaquim; Aziznejad, Shayan; Unser, Michael
Published in: IEEE Open Journal of Signal Processing, Issue vol. 3, 2022, Page(s) pp. 36–48, ISSN 2644-1322
Publisher: IEEE
DOI: 10.1109/ojsp.2021.3136488

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

Author(s): Parhi, Rahul; Unser, Michael
Published in: IEEE Signal Processing Letters, Issue vol. 30, 2023, Page(s) pp. 568–572, ISSN 1558-2361
Publisher: IEEE
DOI: 10.1109/lsp.2023.3275916

Measuring Complexity of Learning Schemes Using Hessian-Schatten Total Variation

Author(s): Aziznejad, Shayan; Campos, Joaquim; Unser, Michael
Published in: SIAM Journal on Mathematics of Data Science, Issue vol. 5, no. 2, 2023, Page(s) 422-445, ISSN 2577-0187
Publisher: SIAM
DOI: 10.1137/22m147517x

A Constrained Method for Lensless Coherent Imaging of Thin Samples

Author(s): Soulez, Ferréol; Rostykus, Manon; Moser, Christophe; Unser, Michael
Published in: Applied Optics, Issue 61(9), 2022, Page(s) F34-F46, ISSN 2155-3165
Publisher: Optica Publishing Group
DOI: 10.1364/ao.445078

Deep Learning Meets Sparse Regularization

Author(s): Parhi, Rahul; Nowak, Robert D.
Published in: IEEE Signal Processing Magazine, Issue vol. 40, no. 6, 2023, Page(s) pp. 63–74, ISSN 1053-5888
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/msp.2023.3286988

Dynamic Fourier ptychography with deep spatiotemporal priors

Author(s): Pakshal Bohra; Thanh-an Pham; Yuxuan Long; Jaejun Yoo; Michael Unser
Published in: Crossref, Issue 6, 2023, ISSN 1361-6420
Publisher: Purpose-Led Publishing
DOI: 10.1088/1361-6420/acca72

A Neural-Network-Based Convex Regularizer for Inverse Problems

Author(s): Alexis Goujon; Sebastian Neumayer; Pakshal Bohra; Stanislas Ducotterd; Michael Unser
Published in: Crossref, Issue 11, 2023, Page(s) 781-795, ISSN 2333-9403
Publisher: IEEE
DOI: 10.1109/tci.2023.3306100

Physics-based neural network for non-invasive control of coherent light in scattering media

Author(s): Alexandra d’Arco; Fei Xia; Antoine Boniface; Jonathan Dong; Sylvain Gigan
Published in: Optics Express, Issue 30(17), 2022, Page(s) 30845-30856, ISSN 1094-4087
Publisher: Optical Society of America
DOI: 10.1364/oe.465702

Dynamic Fourier Ptychography with Deep Spatiotemporal Priors

Author(s): Bohra, Pakshal; Pham, Thanh-an; Long, Yuxuan; Yoo, Jaejun; Unser, Michael
Published in: Dynamic Fourier Ptychography with Deep Spatiotemporal Priors, Issue vol. 39, no. 6, 2023, Page(s) paper no. 064005, ISSN 1361-6420
Publisher: Purpose-LED Publishng
DOI: 10.1088/1361-6420/acca72

Approximation of Lipschitz Functions using Deep Spline Neural Networks

Author(s): Neumayer, Sebastian; Goujon, Alexis; Bohra, Pakshal; Unser, Michael
Published in: SIAM Journal on Mathematics of Data Science, Issue vol. 5, no. 2, 2023, Page(s) 306-322, ISSN 2577-0187
Publisher: SIAM
DOI: 10.1137/22m1504573

Stability of Image-Reconstruction Algorithms

Author(s): del Aguila Pla, Pol; Neumayer, Sebastian Jonas; Unser, Michael;
Published in: IEEE Transactions on Computational Imaging, Issue 9, 2023, Page(s) 1-12, ISSN 2573-0436
Publisher: IEEE
DOI: 10.1109/tci.2023.3236161

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

Author(s): Jonathan Dong; Lorenzo Valzania; Antoine Maillard; Thanh-an Pham; Sylvain Gigan; Michael Unser
Published in: IEEE Signal Processing Magazine, Issue 40(1), 2023, Page(s) 45-57, ISSN 1053-5888
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/msp.2022.3219240

Convex Optimization in Sums of Banach Spaces

Author(s): Unser, Michael; Aziznejad, Shayan
Published in: Applied and Computational Harmonic Analysis, Issue 56, 2022, Page(s) 1-25, ISSN 1063-5203
Publisher: Academic Press
DOI: 10.1016/j.acha.2021.07.002

Sparsest Univariate Learning Models Under Lipschitz Constraint

Author(s): Michael Unser; Shayan Aziznejad; Thomas Debarre
Published in: IEEE Open Journal of Signal Processing, Issue 3, 2022, Page(s) 140-154, ISSN 2644-1322
Publisher: IEEE
DOI: 10.1109/ojsp.2022.3157082

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

Author(s): Goujon, Alexis; Neumayer, Sebastian; Unser, Michael
Published in: SIAM Journal on Imaging Sciences, Issue vol. 17, no. 1, 2024, Page(s) pp. 91–115, ISSN 1936-4954
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/23m1565243

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

Author(s): Rahul Parhi; Michael Unser
Published in: Crossref, Issue 4, 2023, Page(s) 568-572, ISSN 1558-2361
Publisher: IEEE
DOI: 10.1109/lsp.2023.3275916

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

Author(s): Bohra, Pakshal; del Aguila Pla, Pol; Giovanelli, Jean-François; Unser, Michael
Published in: IEEE Transactions on Signal Processing, Issue 71, 2023, Page(s) 2043-2055, ISSN 1941-0476
Publisher: IEEE
DOI: 10.1109/tsp.2023.3282062

Bayesian Inversion for Nonlinear Imaging Models Using Deep Generative Priors

Author(s): Bohra, Pakshal; Pham, Thanh-an; Dong, Jonathan; Unser, Michael
Published in: IEEE Transactions on Computational Imaging, Issue vol. 8, 2022, Page(s) pp. 1237–1249, ISSN 2573-0436
Publisher: IEEE
DOI: 10.1109/tci.2023.3236155

Physics-Based Neural Network for Non-Invasive Control of Coherent Light in Scattering Media

Author(s): d'Arco, Alexandra; Xia, Fei; Boniface, Antoine; Dong, Jonathan; Gigan, Sylvain
Published in: Optics Express, Issue vol. 30, no. 17,, 2022, Page(s) pp. 30845–30856, ISSN 1094-4087
Publisher: Optical Society of America
DOI: 10.1364/oe.465702

A Neural-Network-Based Convex Regularizer for Inverse Problems

Author(s): Goujon, Alexis; Neumayer, Sebastian; Bohra, Pakshal; Unser, Michael
Published in: IEEE Transactions on Computational Imaging, Issue vol. 9, 2023, Page(s) pp. 781–795, ISSN 2333-9403
Publisher: IEEE
DOI: 10.1109/tci.2023.3306100

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions

Author(s): Ducotterd, Stanislas; Goujon, Alexis; Bohra, Pakshal; Perdios, Dimitris; Neumayer, Sebastian; Unser, Michael
Published in: Journal of Machine Learning Research, Issue vol. 25, no. 65, 2024, Page(s) pp. 1–30, ISSN 1532-4435
Publisher: MIT Press

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Author(s): Unser, Michael
Published in: Foundations of Computational Mathematics, 2023, ISSN 1615-3383
Publisher: Springer
DOI: 10.1007/s10208-023-09624-9

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

Author(s): Pourya, Mehrsa; Goujon, Alexis; Unser, Michael
Published in: IEEE Open Journal of Signal Processing, Issue 4, 2023, Page(s) 167-178, ISSN 2644-1322
Publisher: IEEE
DOI: 10.1109/ojsp.2023.3250104

Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priors

Author(s): Pakshal Bohra; Thanh-an Pham; Jonathan Dong; Michael Unser
Published in: IEEE Transactions on Computational Imaging, Issue 8, 2022, Page(s) 1237-1249, ISSN 2573-0436
Publisher: IEEE
DOI: 10.1109/tci.2023.3236155

Sparsest Univariate Learning Models Under Lipschitz Constraint

Author(s): Aziznejad, Shayan; Debarre, Thomas; Unser, Michael
Published in: IEEE Open Journal of Signal Processing, Issue vol. 3, 2022, Page(s) pp. 140–154, ISSN 2644-1322
Publisher: IEEE
DOI: 10.1109/ojsp.2022.3157082

Asymptotic Stability in Reservoir Computing

Author(s): Dong, Jonathan Yuelin; Börve, Erik; Rafayelyan, Mushegh; Unser, Michael;
Published in: Proceedings of the 2022 International Joint Conference on Neural Networks, Issue July 18-23, 2022
Publisher: IEEE
DOI: 10.1109/ijcnn55064.2022.9892302

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