Related papers: Structure Preserving Algorithms for Quaternion Out…

Low-rank quaternion tensor completion method, a novel approach to recovery color videos and images is proposed in this paper. We respectively reconstruct a color image and a color video as a quaternion matrix (second-order tensor) and a…

Gradient descent optimizations and backpropagation are the most common methods for training neural networks, but they are computationally expensive for real time applications, need high memory resources, and are difficult to converge for…

A basic theory on the first order right and left linear quaternion differential systems (LQDS) is given systematic in this paper. To proceed the theory of LQDS we adopt the theory of column-row determinants recently introduced by the…

The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix…

Polarization is a unique characteristic of transverse wave and is represented by Stokes parameters. Analysis of polarization states can reveal valuable information about the sources. In this paper, we propose a separable low-rank quaternion…

This paper presents a randomized quaternion singular value decomposition (QSVD) algorithm for low-rank matrix approximation problems, which are widely used in color face recognition, video compression, and signal processing problems. With…

Contemporary state-of-the-art neural networks have increasingly large numbers of parameters, which prevents their deployment on devices with limited computational power. Pruning is one technique to remove unnecessary weights and reduce…

An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and…

Quaternions are important for a wide variety of rotation-related problems in computer graphics, machine vision, and robotics. We study the nontrivial geometry of the relationship between quaternions and rotation matrices by exploiting the…

Deep learning for predicting or generating 3D human pose sequences is an active research area. Previous work regresses either joint rotations or joint positions. The former strategy is prone to error accumulation along the kinematic chain,…

In this paper, we propose a lower rank quaternion decomposition algorithm and apply it to color image inpainting. We introduce a concise form for the gradient of a real function in quaternion matrix variables. The optimality conditions of…

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

This article investigates Kak neural networks, which can be instantaneously trained, for complex and quaternion inputs. The performance of the basic algorithm has been analyzed and shown how it provides a plausible model of human perception…

Known algorithms for manipulating octagons do not preserve their sparsity, leading typically to quadratic or cubic time and space complexities even if no relation among variables is known when they are all bounded. In this paper, we present…

In recent years, hyper-complex deep networks (such as complex-valued and quaternion-valued neural networks) have received a renewed interest in the literature. They find applications in multiple fields, ranging from image reconstruction to…

We present a novel approach for solving articulated inverse kinematic problems (e.g., character structures) by means of an iterative dual-quaternion and exponentialmapping approach. As dual-quaternions are a break from the norm and offer a…

For many years, channels of a color image have been processed individually, or the image has been converted to grayscale one with respect to color image processing. Pure quaternion representation of color images solves this issue as it…

Transforms using random matrices have been found to have many applications. We are concerned with the projection of a signal onto Gaussian-distributed random orthogonal bases. We also would like to easily invert the process through…

New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…