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In this paper, we modify and apply the recently introduced Mixed Newton Method, which is originally designed for minimizing real-valued functions of complex variables, to the minimization of real-valued functions of real variables by…

Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning…

Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…

We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level…

The authors' paper in Optimization 63 (2014), 505-533, see Ref. [5], was the first one to provide detailed optimality conditions for pessimistic bilevel optimization. The results there were based on the concept of the two-level optimal…

Imaging is a standard example of an inverse problem, where the task of reconstructing a ground truth from a noisy measurement is ill-posed. Recent state-of-the-art approaches for imaging use deep learning, spearheaded by unrolled and…

This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower level frontier-type mapping in order to replace the hierarchical model of two interdependent multiobjective optimization…

Image registration has traditionally been done using two distinct approaches: learning based methods, relying on robust deep neural networks, and optimization-based methods, applying complex mathematical transformations to warp images…

Methods for automated retinal vessel segmentation play an important role in the treatment and diagnosis of many eye and systemic diseases. With the fast development of deep learning methods, more and more retinal vessel segmentation methods…

Adversarial machine learning concerns situations in which learners face attacks from active adversaries. Such scenarios arise in applications such as spam email filtering, malware detection and fake image generation, where security methods…

Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…

Deep learning based approaches are now widely used across biophysics to help automate a variety of tasks including image segmentation, feature selection, and deconvolution. However, the presence of multiple competing deep learning…

Multiple instance (MI) learning with a convolutional neural network enables end-to-end training in the presence of weak image-level labels. We propose a new method for aggregating predictions from smaller regions of the image into an…

The increasing availability of massive data sets poses a series of challenges for machine learning. Prominent among these is the need to learn models under hardware or human resource constraints. In such resource-constrained settings, a…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

We learn about the world from a diverse range of sensory information. Automated systems lack this ability as investigation has centred on processing information presented in a single form. Adapting architectures to learn from multiple…

Nowadays, due to advanced digital imaging technologies and internet accessibility to the public, the number of generated digital images has increased dramatically. Thus, the need for automatic image enhancement techniques is quite apparent.…

The rapid evolution of deep learning has significantly advanced the field of medical image analysis. However, despite these achievements, the further enhancement of deep learning models for medical image analysis faces a significant…

Signal models based on sparsity, low-rank and other properties have been exploited for image reconstruction from limited and corrupted data in medical imaging and other computational imaging applications. In particular, sparsifying…

Deep learning has been achieving decent performance in computer vision requiring a large volume of images, however, collecting images is expensive and difficult in many scenarios. To alleviate this issue, many image augmentation algorithms…