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In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly…

Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…

Proper regularization is crucial in inverse problems to achieve high-quality reconstruction, even with an ill-conditioned measurement system. This is particularly true for three-dimensional photoacoustic tomography, which is computationally…

Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…

Dynamical models identified from data are frequently employed in control system design. However, decoupling system identification from controller synthesis can result in situations where no suitable controller exists after a model has been…

Reconstructing training data from trained neural networks is an active area of research with significant implications for privacy and explainability. Recent advances have demonstrated the feasibility of this process for several data types.…

Recently, data-driven techniques have demonstrated remarkable effectiveness in addressing challenges related to MR imaging inverse problems. However, these methods still exhibit certain limitations in terms of interpretability and…

Data normalization is one of the most important preprocessing steps when building a machine learning model, especially when the model of interest is a deep neural network. This is because deep neural network optimized with stochastic…

We develop a new method for regularising neural networks. We learn a probability distribution over the activations of all layers of the model and then insert imputed values into the network during training. We obtain a posterior for an…

We develop regularisation theory for dynamic inverse problems, solved using online methods with an infinite time horizon. Using concepts of subregularity to treat nonsmooth regularisers, we prove that time-averaged reconstruction errors…

Advancements in parallel processing have lead to a surge in multilayer perceptrons' (MLP) applications and deep learning in the past decades. Recurrent Neural Networks (RNNs) give additional representational power to feedforward MLPs by…

Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…

Despite apparent human-level performances of deep neural networks (DNN), they behave fundamentally differently from humans. They easily change predictions when small corruptions such as blur and noise are applied on the input (lack of…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…

Model regularization requires extensive manual tuning to balance complexity against overfitting. Cross-regularization resolves this tradeoff by directly adapting regularization parameters through validation gradients during training. The…

In phase retrieval and similar inverse problems, the stability of solutions across different noise levels is crucial for applications. One approach to promote it is using signal priors in a form of a generative model as a regularization, at…

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural…

Sequence modeling with neural networks has lead to powerful models of symbolic music data. We address the problem of exploiting these models to reach creative musical goals, by combining with human input. To this end we generalise previous…

Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…