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An extendable, efficient and explainable Machine Learning approach is proposed to represent cyclic plasticity and replace conventional material models based on the Radial Return Mapping algorithm. High accuracy and stability by means of a…
Recent works in deep-learning have shown that second-order information is beneficial in many computer-vision tasks. Second-order information can be enforced both in the spatial context and the abstract feature dimensions. In this work, we…
Recent works in medical image registration have proposed the use of Implicit Neural Representations, demonstrating performance that rivals state-of-the-art learning-based methods. However, these implicit representations need to be optimized…
Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…
Variational methods have become an important kind of methods in signal and image restoration - a typical inverse problem. One important minimization model consists of the squared $\ell_2$ data fidelity (corresponding to Gaussian noise) and…
In the context of the optimization of Deep Neural Networks, we propose to rescale the learning rate using a new technique of automatic differentiation. This technique relies on the computation of the {\em curvature}, a second order…
Analyzing periodic video sequences is a key topic in applications such as automatic production systems, remote sensing, medical applications, or physical training. An example is counting repetitions of a physical exercise. Due to the…
The one-dimensional version of the higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [4] is analyzed. A suitable functional framework in which the minimization problem is well posed is…
Wavefront sensing and reconstruction are widely used for adaptive optics, aberration correction, and high-resolution optical phase imaging. Traditionally, interference and/or microlens arrays are used to convert the optical phase into…
The success and generalisation of deep learning algorithms heavily depend on learning good feature representations. In medical imaging this entails representing anatomical information, as well as properties related to the specific imaging…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…
We are interested in restoring images having values in a symmetric Hadamard manifold by minimizing a functional with a quadratic data term and a total variation like regularizing term. To solve the convex minimization problem, we extend the…
We sketch an application of proximal algorithms to the deformation of de Rham currents into cycles, which is presented as a convex optimization problem. Emphasis is placed on the use of total variation denoising for differential forms,…
Second-order optimizers hold intriguing potential for deep learning, but suffer from increased cost and sensitivity to the non-convexity of the loss surface as compared to gradient-based approaches. We introduce a coordinate descent method…
In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…
Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC…
Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…
In the past years modern mathematical methods for image analysis have led to a revolution in many fields, from computer vision to scientific imaging. However, some recently developed image processing techniques successfully exploited by…
We consider the problem of reconstructing 2D images from randomly under-sampled confocal microscopy samples. The well known and widely celebrated total variation regularization, which is the L1 norm of derivatives, turns out to be…