Related papers: A Fast Algorithm for Cosine Transform Based Tensor…

The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

This article is about an image transform called 3D-DCT, or three-dimensional discrete cosine transform. This is an extension of the well-known 1D and 2D-DCT, which is extensively used, mostly in multimedia coding. A modification of 1D-DCT…

We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…

Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…

This paper presents stable, radix-2, completely recursive discrete cosine transformation algorithms DCT-I and DCT-III solely based on DCT-I, DCT-II, DCT-III, and DCT-IV having sparse and orthogonal factors. Error bounds for computing the…

In this paper, we consider the tensor completion problem, which has many researchers in the machine learning particularly concerned. Our fast and precise method is built on extending the $L_{2,1}$-norm minimization and Qatar Riyal…

Recent advances in computing such as the massively parallel GPUs (Graphical Processing Units),coupled with the need to store and deliver large quantities of digital data especially images, has brought a number of challenges for Computer…

We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…

Diffusion transformer (DiT) models have achieved remarkable success in image generation, thanks for their exceptional generative capabilities and scalability. Nonetheless, the iterative nature of diffusion models (DMs) results in high…

The fully-connected tensor network (FCTN) decomposition has recently exhibited strong modeling capabilities by connecting every pair of tensor factors, thereby capturing rich cross-mode correlations. However, this advantage comes with an…

Recently, a quaternion tensor product named Qt-product was proposed, and then the singular value decomposition and the rank of a third-order quaternion tensor were given. From a more applicable perspective, we extend the Qt-product and…

The quantum Fourier transform for discrete variable (dvQFT) is an efficient algorithm for several applications. It is usually considered for the processing of quantum bits (qubits) and its efficient implementation is obtained with two…

This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

An area efficient row-parallel architecture is proposed for the real-time implementation of bivariate algebraic integer (AI) encoded 2-D discrete cosine transform (DCT) for image and video processing. The proposed architecture computes…

We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…

Linear block transform coding remains a fundamental component of image and video compression. Although the Discrete Cosine Transform (DCT) is widely employed in all current compression standards, its sub-optimality has sparked ongoing…

Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…

The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…