Related papers: Combining physics-based modeling and deep learning…

Many techniques have been proposed for image reconstruction in medical imaging that aim to recover high-quality images especially from limited or corrupted measurements. Model-based reconstruction methods have been particularly popular…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

The deep learning recipe of casting real-world problems as mathematical optimisation and tackling the optimisation by training deep neural networks using gradient-based optimisation has undoubtedly proven to be a fruitful one. The…

Ultrasound reflection tomography is widely used to image large complex specimens that are only accessible from a single side, such as well systems and nuclear power plant containment walls. Typical methods for inverting the measurement rely…

In this paper we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are…

Deep generative models have emerged as promising tools for detecting arbitrary anomalies in data, dispensing with the necessity for manual labelling. Recently, autoregressive transformers have achieved state-of-the-art performance for…

The strength of machine learning models stems from their ability to learn complex function approximations from data; however, this strength also makes training deep neural networks challenging. Notably, the complex models tend to memorize…

In this paper, we propose to solve a regularized distributionally robust learning problem in the decentralized setting, taking into account the data distribution shift. By adding a Kullback-Liebler regularization function to the robust…

Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…

Bilinear models that decompose dynamic data to spatial and temporal factors are powerful and memory-efficient tools for the recovery of dynamic MRI data. These methods rely on sparsity and energy compaction priors on the factors to…

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…

We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

The simplicity of gradient descent (GD) made it the default method for training ever-deeper and complex neural networks. Both loss functions and architectures are often explicitly tuned to be amenable to this basic local optimization. In…

We investigate geometric regularization strategies for learned latent representations in encoder--decoder reduced-order models. In a fixed experimental setting for the advection--diffusion--reaction (ADR) equation, we model latent dynamics…

Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a…

Endmember (EM) spectral variability can greatly impact the performance of standard hyperspectral image analysis algorithms. Extended parametric models have been successfully applied to account for the EM spectral variability. However, these…

Model-based optimization methods and discriminative learning methods have been the two dominant strategies for solving various inverse problems in low-level vision. Typically, those two kinds of methods have their respective merits and…

Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it…