Related papers: QuatIca: Advanced Numerical Linear Algebra and Opt…
This paper presents \textsc{hankel}, a pure-python code for solving Hankel-type integrals and transforms. Such transforms are common in the physical sciences, especially appearing as the radial solution to angularly symmetric Fourier…
We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…
Sequential quadratic programming (SQP) methods have been remarkably successful in solving a broad range of nonlinear optimization problems. These methods iteratively construct and solve quadratic programming (QP) subproblems to compute…
Randomized smoothing is currently the state-of-the-art method that provides certified robustness for deep neural networks. However, due to its excessively conservative nature, this method of incomplete verification often cannot achieve an…
Background and Objective: Deep learning enables tremendous progress in medical image analysis. One driving force of this progress are open-source frameworks like TensorFlow and PyTorch. However, these frameworks rarely address issues…
In many scientific fields like e.g. neuroscience, climatology or physics, complex relationships can be described most parsimoniously by nonlinear mechanics. Despite their relevance, many scientists still apply linear estimates in order to…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
This work presents Kornia -- an open source computer vision library which consists of a set of differentiable routines and modules to solve generic computer vision problems. The package uses PyTorch as its main backend both for efficiency…
In recent years, several models using Quaternion-Valued Convolutional Neural Networks (QCNNs) for different problems have been proposed. Although the definition of the quaternion convolution layer is the same, there are different…
Radiomics enables the extraction of quantitative biomarkers from medical images for precision modeling, but reproducibility and scalability remain limited due to heterogeneous software implementations and incomplete adherence to standards.…
Image reconstruction in Magnetic Resonance Imaging (MRI) is fundamentally a linear inverse problem, such that the image can be recovered via explicit pseudoinversion of the encoding matrix by solving $\textbf{data} = \textbf{Encode} \times…
Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause…
Hypercomplex image processing extends conventional techniques in a unified paradigm encompassing algebraic and geometric principles. This work leverages quaternions and the two-dimensional orthogonal planes split framework (splitting of a…
Designing efficient quasi-Newton methods is an important problem in nonlinear optimization and the solution of systems of nonlinear equations. From the perspective of the matrix approximation process, this paper presents a unified framework…
As hybrid quantum-classical models gain traction in machine learning, there is a growing need for tools that assess their effectiveness beyond raw accuracy. We present QMetric, a Python package offering a suite of interpretable metrics to…
Computer algebra systems play an important role in science as they facilitate the development of new theoretical models. The resulting symbolic equations are often implemented in a compiled programming language in order to provide fast and…
Image Quality Assessment (IQA) metrics are widely used to quantitatively estimate the extent of image degradation following some forming, restoring, transforming, or enhancing algorithms. We present PyTorch Image Quality (PIQ), a…
Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A…
Convex variational problems arise in many fields ranging from image processing to fluid and solid mechanics communities. Interesting applications usually involve non-smooth terms which require well-designed optimization algorithms for their…
Night photography often struggles with challenges like low light and blurring, stemming from dark environments and prolonged exposures. Current methods either disregard priors and directly fitting end-to-end networks, leading to…