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In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…
Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…
Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…
In this paper we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep neural networks. In particular, starting from a concrete min-max distributionally robust…
Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…
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…
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…
Deep neural networks suffer from catastrophic forgetting, where performance on previous tasks degrades after training on a new task. This issue arises due to the model's tendency to overwrite previously acquired knowledge with new…
Using weight decay to penalize the L2 norms of weights in neural networks has been a standard training practice to regularize the complexity of networks. In this paper, we show that a family of regularizers, including weight decay, is…
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…
We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…
Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key contribution is a control-theoretic regularizer for dynamics fitting rooted in the notion of…
This paper investigates the so-called reward-balancing methods, a novel class of algorithms for solving discounted-return reinforcement learning (RL) problems. These methods consist of iteratively adjusting the reward function to transform…
Deep neural networks provide excellent performance for inverse problems such as denoising. However, neural networks can be sensitive to adversarial or worst-case perturbations. This raises the question of whether such networks can be…
Lossy image compression networks aim to minimize the latent entropy of images while adhering to specific distortion constraints. However, optimizing the neural network can be challenging due to its nature of learning quantized latent…
While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators,…