Related papers: Batch-efficient EigenDecomposition for Small and M…

The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the…

A novel energy-efficient edge computing paradigm is proposed for real-time deep learning-based image upsampling applications. State-of-the-art deep learning solutions for image upsampling are currently trained using either resize or…

In this work, we propose a method for the compression of the coupling matrix in volume\hyp surface integral equation (VSIE) formulations. VSIE methods are used for electromagnetic analysis in magnetic resonance imaging (MRI) applications,…

We describe an interface and an implementation for performing Kronecker product actions on NVIDIA GPUs for multiple small 2-D matrices and 3-D arrays processed in parallel as a batch. This method is suited to cases where the Kronecker…

A common strategy for Parameter-Efficient Fine-Tuning (PEFT) of pre-trained Vision Transformers (ViTs) involves adapting the model to downstream tasks by learning a low-rank adaptation matrix. This matrix is decomposed into a product of…

Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible…

Fast computation of singular value decomposition (SVD) is of great interest in various machine learning tasks. Recently, SVD methods based on randomized linear algebra have shown significant speedup in this regime. This paper attempts to…

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…

Deep Learning (DL) methods can reconstruct highly accelerated magnetic resonance imaging (MRI) scans, but they rely on application-specific large training datasets and often generalize poorly to out-of-distribution data. Self-supervised…

Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods. In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and…

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power…

We present a novel computational approach to fast and memory-efficient deformable image registration. In the variational registration model, the computation of the objective function derivatives is the computationally most expensive…

A variety of dimensionality reduction techniques have been applied for computations involving large matrices. The underlying matrix is randomly compressed into a smaller one, while approximately retaining many of its original properties. As…

Direct automatic segmentation of objects from 3D medical imaging, such as magnetic resonance (MR) imaging, is challenging as it often involves accurately identifying a number of individual objects with complex geometries within a large…

Standard rank-revealing factorizations such as the singular value decomposition and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms…

Modern electron tomography has progressed to higher resolution at lower doses by leveraging compressed sensing methods that minimize total variation (TV). However, these sparsity-emphasized reconstruction algorithms introduce tunable…

We study the stochastic Riemannian gradient algorithm for matrix eigen-decomposition. The state-of-the-art stochastic Riemannian algorithm requires the learning rate to decay to zero and thus suffers from slow convergence and sub-optimal…

Deep learning networks are being developed in every stage of the MRI workflow and have provided state-of-the-art results. However, this has come at the cost of increased computation requirement and storage. Hence, replacing the networks…

Fast and accurate MRI reconstruction is a key concern in modern clinical practice. Recently, numerous Deep-Learning methods have been proposed for MRI reconstruction, however, they usually fail to reconstruct sharp details from the…

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…