Related papers: Nonparametric Matrix Response Regression with Appl…
In this paper, we investigate image reconstruction for dynamic Computed Tomography. The motion of the target with respect to the measurement acquisition rate leads to highly resolved in time but highly undersampled in space measurements.…
Individual Neurons in the nervous systems exploit various dynamics. To capture these dynamics for single neurons, we tune the parameters of an electrophysiological model of nerve cells, to fit experimental data obtained by calcium imaging.…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
In safety-critical applications like medical diagnosis, certainty associated with a model's prediction is just as important as its accuracy. Consequently, uncertainty estimation and reduction play a crucial role. Uncertainty in predictions…
The reconstruction of dynamic positron emission tomography (PET) images from noisy projection data is a significant but challenging problem. In this paper, we introduce an unsupervised learning approach, Non-negative Implicit Neural…
Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the…
The meteoric rise in the adoption of deep neural networks as computational models of vision has inspired efforts to "align" these models with humans. One dimension of interest for alignment includes behavioral choices, but moving beyond…
Two-photon imaging of calcium indicators allows simultaneous recording of responses of hundreds of neurons over hours and even days, but provides a relatively indirect measure of their spiking activity. Existing deconvolution algorithms…
While the interaction of ultra-intense ultra-short laser pulses with near- and overcritical plasmas cannot be directly observed, experimentally accessible quantities (observables) often only indirectly give information about the underlying…
Adaptive nuclear-norm penalization is proposed for low-rank matrix approximation, by which we develop a new reduced-rank estimation method for the general high-dimensional multivariate regression problems. The adaptive nuclear norm of a…
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…
Traditional computational methods, such as the finite element analysis, have provided valuable insights into uncovering the underlying mechanisms of brain physical behaviors. However, precise predictions of brain physics require effective…
Nuclear magnetic resonance (NMR) spectroscopy provides detailed information pertaining to dynamic processes through line-shape changes, which have been traditionally limited to equilibrium conditions. However, there is a wealth of…
Ultrasound and radar signals are highly beneficial for medical imaging as they are non-invasive and non-ionizing. Traditional imaging techniques have limitations in terms of contrast and physical interpretation. Quantitative medical imaging…
Dynamic magnetic resonance imaging (dMRI) captures temporally-resolved anatomy but is often challenged by limited sampling and motion-induced artifacts. Conventional motion-compensated reconstructions typically rely on pre-estimated optical…
The human brain is a complex system requiring both macroscopic and microscopic components for comprehensive understanding. However, mapping nonlinear relationships between these scales remains challenging due to technical limitations and…
A key property of neural networks is their capacity of adapting to data during training. Yet, our current mathematical understanding of feature learning and its relationship to generalization remain limited. In this work, we provide a…
Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…