Zobrazeno 1 - 10
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pro vyhledávání: '"A. Unser"'
Localization microscopy enables imaging with resolutions that surpass the conventional optical diffraction limit. Notably, the MINFLUX method achieves super-resolution by shaping the excitation point-spread function (PSF) to minimize the required pho
Externí odkaz:
http://arxiv.org/abs/2410.03349
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they are computa
Externí odkaz:
http://arxiv.org/abs/2409.05734
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the second-orde
Externí odkaz:
http://arxiv.org/abs/2408.13114
Autor:
Unser, Michael, Ducotterd, Stanislas
We first establish a kernel theorem that characterizes all linear shift-invariant (LSI) operators acting on discrete multicomponent signals. This result naturally leads to the identification of the Parseval convolution operators as the class of energ
Externí odkaz:
http://arxiv.org/abs/2408.09981
Autor:
Herbreteau, Sébastien, Unser, Michael
Supervised deep learning has become the method of choice for image denoising. It involves the training of neural networks on large datasets composed of pairs of noisy and clean images. However, the necessity of training data that are specific to the
Externí odkaz:
http://arxiv.org/abs/2407.17399
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theoretically. I
Externí odkaz:
http://arxiv.org/abs/2407.06608
Optoacoustic (OA) imaging combined with reversibly photoswitchable proteins has emerged as a promising technology for the high-sensitivity and multiplexed imaging of cells in live tissues in preclinical research. Through carefully-designed illuminati
Externí odkaz:
http://arxiv.org/abs/2405.15360
We consider a large class of shallow neural networks with randomly initialized parameters and rectified linear unit activation functions. We prove that these random neural networks are well-defined non-Gaussian processes. As a by-product, we demonstr
Externí odkaz:
http://arxiv.org/abs/2405.10229
Autor:
Parhi, Rahul, Unser, Michael
We investigate the function-space optimality (specifically, the Banach-space optimality) of a large class of shallow neural architectures with multivariate nonlinearities/activation functions. To that end, we construct a new family of Banach spaces d
Externí odkaz:
http://arxiv.org/abs/2310.03696
Autor:
Parhi, Rahul, Unser, Michael
Publikováno v:
SIAM Journal on Mathematical Analysis, vol. 56, no. 4, pp. 4662-4686, 2024
We investigate the distributional extension of the $k$-plane transform in $\mathbb{R}^d$ and of related operators. We parameterize the $k$-plane domain as the Cartesian product of the Stiefel manifold of orthonormal $k$-frames in $\mathbb{R}^d$ with
Externí odkaz:
http://arxiv.org/abs/2310.01233