Related papers: QuatIca: Advanced Numerical Linear Algebra and Opt…

This paper presents alpaqa, an open-source C++ implementation of an augmented Lagrangian method for nonconvex constrained numerical optimization, using the first-order PANOC algorithm as inner solver. The implementation is packaged as an…

Commutative hypercomplex algebras offer significant advantages over traditional quaternions due to their compatibility with linear algebra techniques and efficient computational implementation, which is crucial for broad applicability. This…

This article introduces quaternion non-negative matrix factorization (QNMF), which generalizes the usual non-negative matrix factorization (NMF) to the case of polarized signals. Polarization information is represented by Stokes parameters,…

We propose a novel quaternion product unit (QPU) to represent data on 3D rotation groups. The QPU leverages quaternion algebra and the law of 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted…

The tensor train rank (TT-rank) has achieved promising results in tensor completion due to its ability to capture the global low-rankness of higher-order (>3) tensors. On the other hand, recently, quaternions have proven to be a very…

Deep learning has brought significant advancements to X-ray Computed Tomography (CT) reconstruction, offering solutions to challenges arising from modern imaging technologies. These developments benefit from methods that combine classical…

Fourier ptychography is a recently developed imaging approach for large field-of-view and high-resolution microscopy. Here we model the Fourier ptychographic forward imaging process using a convolution neural network (CNN) and recover the…

This paper presents a new approach to quadrify a polynomial programming problem, i.e. reduce the polynomial program to a quadratic program, before solving it. The proposed approach, QUAD-RLT, exploits the Reformulation-Linearization…

Real-valued transforms such as the discrete cosine, sine, and Hartley transforms play a central role in classical computing, complementing the Fourier transform in applications from signal and image processing to data compression. However,…

Imaging Mueller polarimetry has already proved its potential for metrology, remote sensing and biomedicine. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms.…

The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be…

This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…

We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalization of matrices of dimension N…

We introduce QSTToolkit, a Python library for performing quantum state tomography (QST) on optical quantum state measurement data. The toolkit integrates traditional Maximum Likelihood Estimation (MLE) with deep learning-based techniques to…

Orthogonal and 1-Lipschitz neural network layers are essential building blocks in robust deep learning architectures, crucial for certified adversarial robustness, stable generative models, and reliable recurrent networks. Despite…

Solving linear systems of polynomial equations is a ubiquitous problem in both mathematics and physics. The standard approach, Gaussian elimination, scales cubically with system size and often constitutes a computational bottleneck. The…

A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…

A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

A general representation of the quaternion gradients presented in the literature is proposed, and an universal update equation for QLMS-like algorithms is obtained. The general update law is used to study the convergence of widely linear…